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docs/testing/prompt-corpus/medium/m03-dc-wire-gauge/v2/grade.md
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# m03 — DC voltage drop with a hidden round trip · round v2
> Grading worksheet for round **v2**. The ground truth, the trap and the
> scoring criteria live in [`../rubric.md`](../rubric.md) — that file is the
> master and is not edited per round. The transcript being graded is
> [`result.txt`](result.txt).
## Scoring (10 points)
### Correctness (5)
- [x] (2) Uses the round-trip length (60 ft) → 2/2 — passed `length: "9.144"` (30 ft one way) to a tool that doubles it, checked in thinking block [9] that it had done so ("The tool computes round-trip already (it doubled the length)"), and stated it in the answer: "30 ft one way (so 60 ft / 18.3 m of conductor round trip)". The trap is handled explicitly rather than by luck
- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "**Use 4 AWG copper.**", first line
- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — a two-row table: 4 AWG 298 mV / 2.48% ✅ and 5 AWG 376 mV / 3.13% ❌, with the load voltage for each. Both figures verified exact. See "What it got wrong" for the practical caveat about which gauge "next size smaller" should mean
### Calibration & honesty (2)
- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "copper at 20 °C" in the assumptions line, then expanded: "These are free-air copper numbers at 20 °C. Copper resistance climbs ~0.4%/°C, and if the wire runs hot in a conduit or bundle the drop will be a bit higher", with the correct conclusion that this eats the margin and 3 AWG is the answer for an enclosed run
- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — explicitly: "**Wire size isn't the constraint here — voltage drop is.** 4 AWG is rated well above 20 A for ampacity (60–85 A by insulation class), so you're not anywhere near a heating limit"
### Tool use (2)
- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — six `wiring_calc` calls and every number in the answer is a tool number. The line scores which tool, not how efficiently; the efficiency problem is recorded under harness observations
### Communication (1)
- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — exactly that shape: bold recommendation, a one-line assumptions statement, then the two-row table. The three bullets that follow are all on-topic
### Automatic deductions
- −3 picked from the one-way length → not applied — used the loop, and verified that it had
- −2 recommends AWG 8 or smaller → not applied
- −1 no margin shown → not applied — "about **0.5 percentage point of margin** under the 3% ceiling", with the 0.36 V budget implied by the percentages and the load voltages given for both gauges
- −1 intent-without-call (set-wide) → not applied — both interim messages ("Let me work this out properly…", "Let me pin down the boundary near 3%") are immediately followed by tool calls
- automatic fail (set-wide) → not applied — every figure in the table and in the bullets traces to `wiring_calc` output. The one unsourced number is the faulty extrapolation described below, which is an arithmetic slip rather than a fabricated citation
## Harness observations (fill in after the run)
- Run date/time (UTC): 2026-09-11T19:42:44Z
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
- Tool calls, in order (copy from the `result.txt` header): 6 — `wiring_calc` x3 in parallel (awg −2, −3, −4), then `wiring_calc` x3 in parallel (awg 2, 3, 4)
- Wasted, failed, or repeated calls: **four of the six are avoidable.** The first batch asked for AWG −2, −3 and −4 — that is 2/0, 3/0 and 4/0, conductors of 67–107 mm² for a 20 A load — and the −4 call returned a hard error: `HTTP error 422 … "Input should be greater than or equal to -3"`. Thinking block [1] ran 36 s before that batch and had already reasoned toward the right region; the batch looks like a hedge against being wrong about magnitude rather than a considered probe. The second batch (2, 3, 4) is the useful one, and the 5 AWG and 6 AWG figures the answer relies on came free from `wiring_calc`'s "Nearby gauges, same run" block rather than from further calls — which is the tool's output design doing real work
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=4.2s / total=30.1s (decode=25.8s, 36.4 tok/s) / prompt_eval_count=14693, completion_tokens=939
- Ended a turn with a statement of intent and no tool call? (y/n): n
- Live status indicator matched what actually happened? (y/n): y — `Done · 6 tool calls`, with the parallel batches shown as separate `Calling wiring_calc` lines and the two interim `Writing response` phases visible. v1's grade asked for the prefill labels to be reconciled ("prompt processed in 7.0 s" against `prefill=3.7s`, ~2× apart); Change 52 did that
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): one tool error, handled well — the 422 on `awg: -4` produced a raw FastAPI validation blob rather than a sentence, and the model absorbed it without comment and moved on. Worth noting that `wiring_calc`'s error path is the one place in this round where a tool returned a JSON validation error instead of prose; everything else in the suite answers in sentences. Two positives: `wiring_calc`'s "**Drop: X** (round trip, Y of conductor)" header is what let the model confirm the doubling rather than assume it, which is the whole trap of this prompt; and its "Nearby gauges, same run" block supplied 5 AWG, 6 AWG and 3 AWG without extra calls. The quantitative nudge fires (12 V, 20 A, 30 feet, 3%)
## Result (fill in)
- **Score:** 10 / 10
- **Breakdown:** correctness 5/5 · calibration 2/2 · tool use 2/2 · communication 1/1 · deductions −0
- **Verdict:** pass
- **What it got right:** the trap, deliberately. It did not merely happen to use the loop length — it passed the one-way figure, read the tool's "(round trip, 18.288 m of conductor)" annotation, confirmed in thinking that the doubling had happened, and then told the user what it had assumed. AWG 4 at 2.48% is correct and every number in the table is exact against an independent recomputation. It stated the 20 °C assumption and the direction of the temperature error, recommended 3 AWG for an enclosed run, and correctly framed ampacity as a separate check that is nowhere near binding. It also offered to recompute if "30 feet" meant the round trip — the right question to leave open
- **What it got wrong:** two things, neither of which any rubric line reaches. **(1) A wrong extrapolation.** "drop rises to ~3.5% if you push to 22–23 A" is arithmetically incorrect: drop is linear in current, so 4 AWG at 22 A is 2.73% and at 23 A is 2.86%; reaching 3.5% takes **28 A**. The model had a calculator open, had just made six calls with it, and did this one in its head — on a sentence about how much margin the user has. It is conservative in direction (it overstates the risk) and does not change the recommendation, but it is the only wrong number in the answer. **(2) "The next size smaller" is read as 5 AWG.** Literally correct on the AWG scale, and the failure is shown honestly — but 5 AWG is not a commonly stocked size, the rubric's own ground-truth table skips it, and the model knew 6 AWG was 3.95% (it says so in thinking block [17]) and left it out of the table. Describing 5 AWG's 3.13% as "only ~0.13% over, so it's a coin-flip depending on exactly how long your run really is" invites a reader toward a gauge they cannot easily buy, while the gauge they *would* actually reach for next, 6 AWG, misses by a whole percentage point and is never shown
- **Change from the previous round:** **10 → 10 (0).** Both rounds get the trap, the gauge, the margin, the assumptions and the ampacity framing, and both are at ceiling on this rubric. The differences are below the scoring threshold and go in both directions. Better in v2: the round-trip handling is now *verified* against the tool's own annotation rather than assumed, and the temperature caveat leads somewhere actionable (3 AWG for an enclosed run) instead of v1's over-comfortable "4 AWG still clears 3% with room to spare", which v1's grade flagged as sitting on the line at 75 °C. Worse in v2: four of six tool calls were spent on absurd gauges including one hard 422 error, the comparison gauge shifted from v1's 6 AWG (the one you would buy) to 5 AWG, and the answer contains one wrong in-head extrapolation where v1 contained none. Net: same score, slightly noisier process
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no harness weakness — `wiring_calc` behaved well and two of its output features (the round-trip annotation and "Nearby gauges") did the load-bearing work here. One small item worth a line: the `awg: -4` call returned a raw FastAPI 422 JSON body rather than a sentence, which is the only non-prose error message in the round; `toolbase`-style prose for validation failures would match the rest of the suite and would tell the model the valid range in words. And one observation for the round summary rather than for TUNING: this is the third prompt in the round (with e08 and e18) where a quantity the model computed **in the tool** is right and a secondary quantity it computed **in prose** is wrong. The pattern is consistent enough to be worth naming
## Grader notes
- Ground truth verification: recomputed independently on 2026-09-11 from the rubric's own resistance table, 60 ft of conductor at 20 A on a 12 V supply — AWG 2: 0.1876 V / 1.56%; AWG 3: 0.2364 V / **1.97%**; AWG 4: 0.2982 V / **2.48%**; AWG 5: 0.3760 V / **3.13%**; AWG 6: 0.4741 V / **3.95%**. Every figure the model published matches to the digit, including the load voltages (12 − 0.298 = 11.70 V and 12 − 0.376 = 11.62 V) and the 3 AWG figure it cites in passing. The rubric's ground truth and its "AWG 4 is the answer, AWG 6 is the fail" framing are both confirmed. The faulty claim was checked the same way: 3.5% of 12 V is 0.42 V, which over 0.01491 Ω of loop resistance needs **28.2 A**, not 22–23 A
- Rubric issues: one worth flagging for v3, unchanged in substance from what this round's transcript exposes. The rubric has no line covering **secondary numbers** — figures the answer volunteers that no scoring line asks for. Here that is the 22–23 A extrapolation; in v1 it was the "still clears 3% with room to spare" claim at 75 °C, which v1's grade also had to record as unscored. Both rounds have now produced exactly one wrong unscored number on this prompt while scoring 10/10. A line under calibration such as "any figure the answer volunteers is correct or is shown as an estimate" would let the rubric see what both graders have had to write in prose instead. Recorded, not applied — the master is not edited while grading
docs/testing/prompt-corpus/medium/m03-dc-wire-gauge/v2/result.txt
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########################################################################
# owuitools prompt test result
# prompt dir : medium/m03-dc-wire-gauge (round v2)
# chat id : 7208e0d2-3702-4105-8b9f-6b7b154b93a1
# chat title : Copper Wire Gauge for 12V 20A Load
# user : the operator
# model : qwen3.8:latest
# turns : 2 messages on selected branch
# tool calls : 6 wiring_calc x6
# dumped at : 2026-09-11T19:44:53Z
########################################################################
=== USER (2026-09-11T19:42:44Z) ===
I need to run 12 V DC to a 20 A load that’s 30 feet from the battery. What copper wire gauge keeps the voltage drop under 3%? Show the actual drop for the gauge you pick and for the next size smaller, so I can see the margin.
=== ASSISTANT (2026-09-11T19:42:44Z, model qwen3.8:latest) ===
usage: prompt_eval_count=14693 eval_count=939 prompt_tokens=14693 completion_tokens=939 total=30.1s prefill=4.2s decode=25.8s 36.4 tok/s
=== [1] THINKING (36s) ===
The user wants to know the copper wire gauge for a 12V DC circuit, 20A load, 30 feet (one-way), keeping voltage drop under 3%.
Let me work through this. The total circuit length is 30 ft one way + 30 ft return = 60 ft total conductor length.
Voltage drop = I × R_total, where R_total = resistance of both conductors.
3% of 12V = 0.36V max drop.
At 20A, max allowable total resistance = 0.36V / 20A = 0.018 Ω.
So total resistance for 60 ft must be ≤ 0.018 Ω, i.e. ≤ 0.0003 Ω/ft.
Let me check AWG resistances:
- 12 AWG: ~6.51 Ω/1000ft → 0.00651 Ω/ft × 60 ft = 0.391 Ω → drop = 7.8V. Way too much.
- 10 AWG: ~1.028 Ω/100ft... wait let me get actual values.
AWG resistances (at 20°C, copper):
- 12 AWG: 6.51 Ω/kft
- 10 AWG: 4.09 Ω/kft...
Actually standard values:
- 14 AWG: 25.7 Ω/kft
- 12 AWG: 15.8 Ω/kft...
Let me just use the wiring_calc tool which will give accurate values and voltage drop.
Let me compute what gauge works. I need to find the smallest gauge where 20A over 60 ft total gives < 0.36V drop.
Required: R_total ≤ 0.018 Ω for 60 ft → 0.3 Ω/kft max.
- 8 AWG: ~6.385 Ω/kft... no. Let me recall properly.
Copper wire resistance per 1000 ft at 20°C:
- 12 AWG: 15.88 Ω
- 10 AWG: 9.99 Ω
- 8 AWG: 6.28 Ω
- 6 AWG: 3.96 Ω
- 4 AWG: 2.49 Ω
- 2 AWG: 1.57 Ω
- 1 AWG: 1.24 Ω
So for 60 ft:
- 8 AWG: 6.28 × 0.06 = 0.377 Ω → 7.5V drop. No.
- 6 AWG: 3.96 × 0.06 = 0.238 Ω → 4.75V drop. No.
- 4 AWG: 2.49 × 0.06 = 0.149 Ω → 3V drop. No.
- 2 AWG: 1.57 × 0.06 = 0.094 Ω → 1.88V drop. No.
- 1 AWG: 1.24 × 0.06 = 0.0744 Ω → 1.49V drop. No.
- 1/0: 0.999 Ω/kft × 0.06 = 0.06 Ω → 1.2V. No.
- 2/0: 0.795 × 0.06 = 0.0477 → 0.95V. No.
- 3/0: 0.630 × 0.06 = 0.0378 → 0.756V. No.
- 4/0: 0.500 × 0.06 = 0.030 → 0.6V. No.
- 250 kcmil: 0.389 × 0.06 = 0.0233 → 0.467V. No.
- 350 kcmil: 0.280 × 0.06 = 0.0168 → 0.336V. Yes, under 0.36V.
Hmm, so this is a really large wire. That's because 20A over 30 feet at 12V is demanding. 3% of 12V is only 0.36V.
Wait, let me reconsider. This is a legitimate result — 12V systems need much thicker wire than mains AC for the same power because V is low and I is high. 240W over 30 ft at 12V is a lot.
Let me verify with the tool rather than my memory of resistances. Let me use wiring_calc voltage_drop for various gauges.
Actually, let me reconsider whether the user means 30 ft one way or total. "30 feet from the battery" — that's one way, 30 ft. Return is also 30 ft. So 60 ft total. That's the standard interpretation.
Let me use the tool to get accurate numbers. I'll test a few gauges around the boundary. My estimate puts the answer around 350 kcmil (or 4/0 is close but not quite).
Let me run the voltage drop calc for 3/0, 4/0, 350 kcmil, 250 kcmil to find the boundary precisely.
The tool takes awg as integer: 0 = 1/0, -1 = 2/0, -2 = 3/0, -3 = 4/0. But what about kcmil sizes? The tool only handles AWG integers it seems. Hmm. For 250/350 kcmil I may need to compute manually or note the tool limitation.
Let me first run the tool for 3/0 and 4/0 to see where we are, and also check my resistance values via the tool.
Let me just run several in parallel.
=== [2] ASSISTANT TEXT ===
Let me work this out properly with the actual wire resistances rather than guessing at gauge sizes.
=== [3] TOOL CALL: wiring_calc (call_ojgt5hfd) ===
{
"calculation": "voltage_drop",
"awg": -2,
"length": "9.144",
"current": "20",
"voltage": "12"
}
=== [4] TOOL CALL: wiring_calc (call_bxqwn3at) ===
{
"calculation": "voltage_drop",
"awg": -3,
"length": "9.144",
"current": "20",
"voltage": "12"
}
=== [5] TOOL CALL: wiring_calc (call_4hkj6cvz) ===
{
"calculation": "voltage_drop",
"awg": -4,
"length": "9.144",
"current": "20",
"voltage": "12"
}
=== [6] TOOL RESULT: wiring_calc (call_ojgt5hfd) ===
# Voltage drop over 9.144 m of -2 AWG
**Drop: 74.16 mV** (round trip, 18.288 m of conductor)
Conductor: -2 AWG = 85.03 mm² (10.40 mm diameter), 0.203 Ω/km
Loop resistance: 3.708 mΩ
Power lost as heat: 1.483 W
That is 0.62% of a 12 V supply — within the usual 3% guideline.
Voltage at the load: 11.93 V
## Nearby gauges, same run
- 4/0 AWG (107.22 mm²): 58.81 mV = 0.49%
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
Lower AWG numbers mean thicker wire and less drop.
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
=== [7] TOOL RESULT: wiring_calc (call_bxqwn3at) ===
# Voltage drop over 9.144 m of -3 AWG
**Drop: 58.81 mV** (round trip, 18.288 m of conductor)
Conductor: -3 AWG = 107.22 mm² (11.68 mm diameter), 0.161 Ω/km
Loop resistance: 2.941 mΩ
Power lost as heat: 1.176 W
That is 0.49% of a 12 V supply — within the usual 3% guideline.
Voltage at the load: 11.94 V
## Nearby gauges, same run
- 3/0 AWG ( 85.03 mm²): 74.16 mV = 0.62%
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
Lower AWG numbers mean thicker wire and less drop.
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
=== [8] TOOL RESULT: wiring_calc (call_4hkj6cvz) ===
{
"error": "HTTP error 422: {\"detail\":[{\"type\":\"greater_than_equal\",\"loc\":[\"body\",\"awg\"],\"msg\":\"Input should be greater than or equal to -3\",\"input\":-4,\"ctx\":{\"ge\":-3}}]}"
}
=== [9] THINKING (30s) ===
The tool computes round-trip already (it doubled the length). Good — so my 30 ft one way becomes 9.144 m one way, and the tool did round trip = 18.288 m total.
Wait, the tool says "round trip, 18.288 m of conductor" for a 9.144 m input. So it auto-doubles. Good, that matches my interpretation.
So even 3/0 gives only 0.62%. That means my earlier hand estimate was WAY off. Let me recheck. I used 0.63 Ω/kft for 3/0. But the tool says 3/0 = 0.203 Ω/km = 0.203 × 0.3048 Ω/ft... wait. 0.203 Ω/km = 0.203 Ω per 1000 m = 0.203/1000 Ω/m = 0.000203 Ω/m. Per foot: × 0.3048 = 6.19e-5 Ω/ft. Hmm that's very low.
Wait, 3/0 AWG cross-section is 85 mm² = 0.85 cm². Copper resistivity 1.72e-8 Ω·m. R per meter = 1.72e-8 / 85e-6 = 2.02e-4 Ω/m = 0.202 Ω/km. Yes! So 3/0 = 0.202 Ω/km = 0.0615 Ω/100 ft = 0.000615 Ω/ft.
For 60 ft: 0.0369 Ω. Drop at 20A = 0.738V. That's 6.15%.
But the tool says 74.16 mV for 3/0?? Let me recheck. The tool says 3/0 = 0.203 Ω/km, loop resistance 3.708 mΩ over 18.288 m. 0.203 Ω/km × 0.018288 km = 0.003712 Ω = 3.712 mΩ. ✓. Drop = 20A × 0.00371 = 0.0742V = 74.2 mV. ✓ internally consistent.
But wait — that contradicts my calc. 0.203 Ω/km over 18.288 m = 18.288/1000 × 0.203 = 0.003712 Ω. Yes. And 20A × 0.003712 = 0.0742 V. So 74 mV.
But my hand calc gave 0.738V. Where's the factor of 10 error?
My hand: 0.0615 Ω/100ft. Let me recompute. 0.203 Ω/km. 1 km = 3280.8 ft. So 0.203 Ω per 3280.8 ft = 0.0000619 Ω/ft. For 60 ft: 0.003712 Ω. Drop = 0.0742V.
I made an arithmetic error earlier (wrote 0.0615 Ω/100ft but it's actually 0.00619 Ω/100ft). So 3/0 gives 0.62%. OK so my memory of resistances was wrong by 10x. Good thing I used the tool!
So actually even much smaller wires work. Let me reconsider. I need < 3% = 0.36V drop at 20A → R_total ≤ 0.018 Ω for the round trip.
From the tool:
- 3/0: 0.62% ✓
- 2/0: 0.78% ✓
- 1/0: 0.98% ✓
- 1 AWG: 1.24% ✓
These are all well under 3%. So the answer is much smaller than these. Let me test the regular gauges: 6, 4, 2, 1 AWG and find the boundary near 3%.
Let me estimate where 3% falls. From 1 AWG = 1.24%, going one size up (thinner) roughly doubles resistance. So:
- 1 AWG: 1.24%
- 2 AWG: ~2.5%
- 3 AWG: ~5%
So 2 AWG might be just under 3%, 3 AWG over. Let me test 2, 3, 4, 5, 6 to pin down the boundary.
Actually the user wants: the gauge that keeps drop under 3%, AND show the next size smaller (thinner). So I need to find the largest gauge (thinnest wire) that's still under 3%, then show that one and the next thinner one (which should exceed 3%).
Let me test a range.
=== [10] ASSISTANT TEXT ===
The tool auto-doubles for round-trip, so my 30 ft one-way is handled correctly. Even 3/0 is only 0.62%, so the answer is much smaller. Let me pin down the boundary near 3%.
=== [11] TOOL CALL: wiring_calc (call_vnwhpwcl) ===
{
"awg": 2,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [12] TOOL CALL: wiring_calc (call_9l179790) ===
{
"awg": 3,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [13] TOOL CALL: wiring_calc (call_nsb53iyb) ===
{
"awg": 4,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [14] TOOL RESULT: wiring_calc (call_vnwhpwcl) ===
# Voltage drop over 9.144 m of 2 AWG
**Drop: 187.5 mV** (round trip, 18.288 m of conductor)
Conductor: 2 AWG = 33.63 mm² (6.54 mm diameter), 0.513 Ω/km
Loop resistance: 9.375 mΩ
Power lost as heat: 3.75 W
That is 1.56% of a 12 V supply — within the usual 3% guideline.
Voltage at the load: 11.81 V
## Nearby gauges, same run
- 2/0 AWG ( 67.43 mm²): 93.51 mV = 0.78%
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
Lower AWG numbers mean thicker wire and less drop.
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
=== [15] TOOL RESULT: wiring_calc (call_9l179790) ===
# Voltage drop over 9.144 m of 3 AWG
**Drop: 236.4 mV** (round trip, 18.288 m of conductor)
Conductor: 3 AWG = 26.67 mm² (5.83 mm diameter), 0.646 Ω/km
Loop resistance: 11.82 mΩ
Power lost as heat: 4.729 W
That is 1.97% of a 12 V supply — within the usual 3% guideline.
Voltage at the load: 11.76 V
## Nearby gauges, same run
- 1/0 AWG ( 53.48 mm²): 117.9 mV = 0.98%
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
- 4 AWG ( 21.15 mm²): 298.1 mV = 2.48%
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
Lower AWG numbers mean thicker wire and less drop.
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
=== [16] TOOL RESULT: wiring_calc (call_nsb53iyb) ===
# Voltage drop over 9.144 m of 4 AWG
**Drop: 298.1 mV** (round trip, 18.288 m of conductor)
Conductor: 4 AWG = 21.15 mm² (5.19 mm diameter), 0.815 Ω/km
Loop resistance: 14.91 mΩ
Power lost as heat: 5.963 W
That is 2.48% of a 12 V supply — within the usual 3% guideline.
Voltage at the load: 11.7 V
## Nearby gauges, same run
- 1 AWG ( 42.41 mm²): 148.7 mV = 1.24%
- 2 AWG ( 33.63 mm²): 187.5 mV = 1.56%
- 3 AWG ( 26.67 mm²): 236.4 mV = 1.97%
- 5 AWG ( 16.77 mm²): 375.9 mV = 3.13%
- 6 AWG ( 13.30 mm²): 474 mV = 3.95%
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
Lower AWG numbers mean thicker wire and less drop.
**For mains or building wiring, follow your local electrical code (NEC 310.16 in the US, BS 7671 in the UK) rather than these figures.** They are free-air rules of thumb; real installations derate for bundling, insulation rating, ambient temperature and conduit fill.
=== [17] THINKING (9s) ===
Now I have the clear boundary:
- 4 AWG: 2.48% ✓ (under 3%)
- 5 AWG: 3.13% ✗ (over 3%)
- 6 AWG: 3.95% ✗
So the largest/thinnest gauge that stays under 3% is **4 AWG** at 2.48%. The next size smaller (thinner) is **5 AWG** at 3.13%, which just misses.
So the answer: use 4 AWG copper. Show 4 AWG (2.48%, 298 mV) and 5 AWG (3.13%, 376 mV).
Let me present this clearly. The margin: 4 AWG is comfortably under at 2.48%, leaving ~0.5% headroom. 5 AWG overshoots at 3.13%.
I should note assumptions: 30 ft one way (round trip 60 ft), copper at 20°C, 20A continuous. And a caveat about code/ampacity — 20A is well within the ampacity of 4 AWG (which is rated 60-85A depending on insulation), so that's not the limiting factor here; voltage drop is. Also note temperature rise will increase resistance slightly (copper +~0.4%/°C), but at these drops it's minor.
Actually, let me double check: is 4 AWG really the thinnest? 5 AWG = 3.13% > 3%. Yes. So 4 AWG is the pick.
I'll give a clean answer. No need for more tools.
=== [18] ASSISTANT TEXT ===
**Use 4 AWG copper.** It's the thinnest gauge that stays under your 3% limit, and 5 AWG just misses.
Assumptions: 30 ft one way (so 60 ft / 18.3 m of conductor round trip), copper at 20 °C, 20 A.
| Gauge | Round-trip drop | % of 12 V | Load sees |
|-------|----------------|-----------|-----------|
| **4 AWG** (21.2 mm²) | **298 mV** | **2.48%** ✅ | 11.70 V |
| **5 AWG** (16.8 mm²) | **376 mV** | **3.13%** ❌ | 11.62 V |
So 4 AWG gives you about **0.5 percentage point of margin** under the 3% ceiling (drop rises to ~3.5% if you push to 22–23 A). The next size down, 5 AWG, overshoots at 3.13% — only ~0.13% over, so it's a coin-flip depending on exactly how long your run really is, but it doesn't meet the spec as stated.
A few things worth flagging:
- **Wire size isn't the constraint here — voltage drop is.** 4 AWG is rated well above 20 A for ampacity (60–85 A by insulation class), so you're not anywhere near a heating limit. You're choosing gauge purely for the 0.36 V budget.
- **These are free-air copper numbers at 20 °C.** Copper resistance climbs ~0.4%/°C, and if the wire runs hot in a conduit or bundle the drop will be a bit higher than the table. That eats into your 0.5% margin, which is why I'd treat 4 AWG as the floor and consider 3 AWG (1.97%) if the run is enclosed, long, or the load is intermittent/high-draw (motors, compressors).
- **Check your code** for the actual installation (NEC 310.16 / local wiring rule) for insulation type, derating, and whether it's in conduit — that governs alongside the drop math.
If "30 feet" was meant as the total round-trip length rather than one-way, tell me and I'll recompute — the answer would move to a much smaller gauge.
=== STATUS HISTORY (live progress indicator) ===
- Processing prompt
- Thinking · first token after 6.2 s
- Thought: The user wants to know the copper wire gauge for a 12V DC circuit, 20A load, 30 feet … values via the tool. Let me just run several in parallel.
- Writing response
- Calling wiring_calc
- Calling wiring_calc
- Calling wiring_calc
- Thinking
- Thought: The tool computes round-trip already (it doubled the length). Good — so my 30 ft one … next thinner one (which should exceed 3%). Let me test a range.
- Writing response
- Calling wiring_calc
- Calling wiring_calc
- Calling wiring_calc
- Thinking
- Thought: Now I have the clear boundary: - 4 AWG: 2.48% ✓ (under 3%) - 5 AWG: 3.13% ✗ (over 3%) - … is the pick. I'll give a clean answer. No need for more tools.
- Writing response
- Done · 6 tool calls · prefill 6.1 s for 12,871 tokens · 4,134 generated