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# m03 — DC voltage drop with a hidden round trip · round v3
> Grading worksheet for round **v3**. 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 — stated before any tool call in the interim message ("I'm reading as **one-way** distance, so the current travels 60 ft of wire total"), passed as `length: "9.144"` to a tool that doubles it, and the doubling confirmed in thinking block [18] ("The tool's voltage_drop uses round trip automatically (it doubled the length to 18.288 m)"). Same deliberate handling as v2
- [x] (2) AWG 4 (or larger with a stated temperature argument) → 2/2 — "**Pick: 4 AWG copper.**", first words
- [x] (1) Shows the comparison gauge's drop and that it fails → 1/1 — a two-row table: 4 AWG 298 mV / 2.48% ✅, **6 AWG** 474 mV / 3.95% ❌, with loop resistance and load voltage for each. This round the comparison gauge is the one a person would actually buy — v2's grade flagged its choice of 5 AWG as literally-next-but-unstockable — and 5 AWG's 3.13% is given in a parenthesis for completeness
### Calibration & honesty (2)
- [x] (1) States the conductor temperature / resistivity assumption → 1/1 — "These are free‑air copper figures; derate if the cable runs hot, bundled, or through conduit for long stretches." The temperature dependence is stated and the figures are identified as the tool's free-air copper values; the explicit "20 °C" v2 wrote is not here. Read as satisfying the line — the assumption and its direction of error are both given — with the omission noted
- [x] (1) Notes ampacity is a separate (easily met) check, or at least does not claim ampacity drove the choice → 1/1 — "**Ampacity is not your constraint here.** 20 A is well inside every gauge's rating (even 10 AWG is rated 30 A), so this is purely a voltage‑drop decision." The 30 A figure is the tool's NEC 60 °C column for 10 AWG
### Tool use (2)
- [x] (2) `wiring_calc`. 1 if `matlab_run` with a correct formula and correct resistance values. 0 if mental. → 2/2 — seven `wiring_calc` calls; every figure in the answer, including the secondary ones, is a tool figure
### Communication (1)
- [x] (1) Gauge first, two drops side by side, one line on assumptions → 1/1 — bold pick with the assumption in the same sentence, then the two-row table, then five short bullets and a rule-of-thumb formula
### Automatic deductions
- −3 picked from the one-way length → not applied
- −2 recommends AWG 8 or smaller → not applied
- −1 no margin shown → not applied — the table, the "~1.5× the drop" step, and the 5 AWG parenthesis all show it
- −1 intent-without-call (set-wide) → not applied — the interim "Let me pull the real resistance figures and compute drops rather than guess" is followed immediately by four calls
- automatic fail (set-wide) → not applied
## Harness observations (fill in after the run)
- Run date/time (UTC): 2026-09-11T23:20:11Z (dumped 23:21:57Z)
- Model tag / Open WebUI version: qwen3.8:latest / Open WebUI 0.11.3
- Tool calls, in order (copy from the `result.txt` header): 7 — `wiring_calc` awg_properties ×4 (4, 6, 8, 10 AWG) in parallel; `wiring_calc` voltage_drop ×3 (4, 6, 8 AWG) in parallel
- Wasted, failed, or repeated calls: no failures (v2 had a 422 on `awg: -4`). The four `awg_properties` calls were unnecessary — `voltage_drop` returns the resistance and a "Nearby gauges" list, so the three drop calls alone carried the answer — but they were cheap and none returned anything absurd
- Prefill time / total time / tokens (from the `usage:` line in `result.txt`): prefill=2.4s / total=28.2s (decode=25.7s, 36.6 tok/s) / prompt_eval_count=14977, completion_tokens=938; status line: 2,781 generated
- 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 — seven `Calling …` lines, `Done · 7 tool calls · prefill 6.0 s for 12,871 tokens · 2,781 generated`
- Anything odd (loops, truncation notices, tool errors, effect of the inlet nudge): the nudge fires (12 V, 20 A, 30 feet). The 27-second first thinking block works the whole problem by hand from remembered resistances, reaches "4 AWG works, 6 AWG does not", and then says "These are from memory - I should use the tool" — compute-then-verify, and the tool agreed to the digit. **Every secondary number in the answer is right this time**: the 1.5× step (474/298 = 1.59), the heat figures (5.96 W, 9.48 W), the round-trip-reinterpretation (6 AWG at 30 ft loop = 1.98%), the 2 AWG headroom figure (1.56%), and the rule-of-thumb formula. v1 and v2 each shipped one wrong unscored number on this prompt; v3 ships none. The `wiring_calc` local-code advisory (in bold in all seven results) is reflected as "derate if the cable runs hot, bundled, or through conduit" — appropriate for a low-voltage DC battery run, where no building code applies
### Change 54 checks (this round's changes — fill in even when they did not fire)
- Did a tool result end with a `Sources:` line? (y/n): n — calculator
- Did the answer carry a URL? (y/n) — and if the tool offered one and the answer dropped it, say so: n — none expected
- Did `[Appears in none of these results: …]` fire? Was it acted on? (n/a if no search): n/a
- Did a `search=` jump report `inside the section '…'`? Did it name the right subject?: n/a
- Did a `search=` miss return the opening of the document? Did the model keep using the source?: n/a
## 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 and with the assumption stated first; AWG 4 with 6 AWG as the honest comparison; every number from the tool, including the volunteered ones; ampacity framed correctly; the "if you meant round trip" case handled with its own figure
- **What it got wrong:** nothing that costs a point. "20 °C" is implied rather than stated; four of seven calls were redundant
- **Change from the previous round:** **10 → 10 (0)**, and the cleanest of the three runs. Both of v2's unscored defects are gone — the comparison gauge is 6 AWG rather than 5, and there is no wrong in-head extrapolation (v2's "3.5% at 22–23 A" has no counterpart; the one extrapolation here, 2 AWG for surge headroom, is a tool figure). Tool use is one call heavier and one failure lighter. Nothing in Change 54 touches this prompt
- **Worth recording in TUNING.md?** (only if it exposes a harness or prompt weakness): no — and worth one positive line against v2's "secondary numbers computed in prose are wrong" pattern: on this prompt, this round, they were all computed in the tool and all right
## Grader notes
- Ground truth verification: as in v2 — 60 ft of conductor at 20 A on 12 V from the rubric's table: AWG 4 0.298 V / 2.48%, AWG 5 0.376 V / 3.13%, AWG 6 0.474 V / 3.95%, AWG 8 0.754 V / 6.28%, AWG 2 0.188 V / 1.56%. Every figure the model published matches. Heat: 20² × 0.01491 = 5.96 W; 20² × 0.0237 = 9.48 W. Rule of thumb Drop = 2·L·I·R is the correct DC loop formula
- Rubric issues: v2's note about secondary numbers stands as a wording suggestion; it was not exercised this round
docs/testing/prompt-corpus/medium/m03-dc-wire-gauge/v3/result.txt
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########################################################################
# owuitools prompt test result
# prompt dir : medium/m03-dc-wire-gauge (round v3)
# chat id : 202f0330-2330-4aaf-ad70-d6c69010c518
# chat title : Copper Wire Gauge for 12V 20A Load
# user : the operator
# model : qwen3.8:latest
# turns : 2 messages on selected branch
# tool calls : 7 wiring_calc x7
# dumped at : 2026-09-11T23:21:57Z
########################################################################
=== USER (2026-09-11T23:20:11Z) ===
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 (2026-09-11T23:20:11Z, model qwen3.8:latest) ===
usage: prompt_eval_count=14977 eval_count=938 prompt_tokens=14977 completion_tokens=938 total=28.2s prefill=2.4s decode=25.7s 36.6 tok/s
=== [1] THINKING (27s) ===
The user wants a wire gauge calculation for 12V DC, 20A load, 30 feet. Voltage drop < 3%.
Let me think about this. The run is 30 feet one way, so total circuit length is 60 feet (round trip).
Voltage drop formula: V_drop = 2 × L × I × R_per_foot (where R is resistance per foot of wire, L is one-way length).
Actually, V_drop = I × R_total where R_total = 2 × L × R_per_foot.
3% of 12V = 0.36V max drop.
Let me use the wiring_calc tool for voltage drop. It takes AWG, length, current, voltage.
Let me check AWG properties and voltage drop. Let me calculate for a few gauges.
Let me think about what gauge would work. For 20A over 60 feet total, we need low resistance.
Let me compute. Resistance per foot (copper):
- 10 AWG: ~1.0 ohm/1000 ft = 0.001 ohm/ft
- 8 AWG: ~0.647 ohm/1000 ft = 0.000647 ohm/ft
- 6 AWG: ~0.407 ohm/1000 ft
For 30 ft one way, round trip 60 ft.
Using 10 AWG: R_total = 60 ft × 0.001 ohm/ft = 0.06 ohm. V_drop = 20A × 0.06 = 1.2V. That's 10% of 12V. Too much.
8 AWG: R_total = 60 × 0.000647 = 0.0388 ohm. V_drop = 20 × 0.0388 = 0.776V. That's 6.5%. Still over 3%.
6 AWG: R_total = 60 × 0.000407 = 0.0244 ohm. V_drop = 20 × 0.0244 = 0.488V. That's 4.07%. Still over 3%!
4 AWG: ~0.253 ohm/1000 ft = 0.000253 ohm/ft. R_total = 60 × 0.000253 = 0.0152 ohm. V_drop = 20 × 0.0152 = 0.304V. That's 2.53%. Under 3%!
So 4 AWG works, 6 AWG does not.
Wait, let me double check the resistance values. These are from memory - I should use the tool. Let me use wiring_calc with awg_properties and voltage_drop.
Actually the question asks to show the actual drop for the gauge I pick AND the next size smaller. So if I pick 4 AWG, show 4 AWG and 6 AWG.
Let me verify with the tools. Let me run awg_properties for 4, 6, 8, 10 and voltage_drop calculations.
Note: the user says "30 feet from the battery" - I'll assume that's one-way distance, so round trip is 60 ft. I should state this assumption clearly.
Let me use the tools. I'll do voltage_drop for 4, 6, 8, 10 AWG with length 30 (one-way? or total?).
Hmm, the voltage_drop tool - I need to check whether it takes one-way or round-trip length. Let me look. The description says "One-way cable length in metres." for length. Wait, it says metres but the user is in feet. Let me check - the tool uses SI (metres). But the user gave feet. Let me convert: 30 ft = 9.144 m.
Actually wait, let me re-read: "length": "One-way cable length in metres." So it takes one-way length in metres and presumably computes round-trip internally. Let me verify by running it.
Let me just run the tools and see what they return. Let me do awg_properties first to get resistance, and voltage_drop.
Actually, let me be careful. Let me run several in parallel:
- awg_properties for 4, 6, 8, 10
- voltage_drop for each with length 9.144 m (30 ft one way), current 20A, voltage 12V
Let me batch these.
Actually, let me reconsider whether the tool does round-trip automatically. I'll run one and check the output, then decide. But to save time, let me run them all and read the outputs carefully.
Let me run awg_properties for 4, 6, 8, 10 in parallel first.
=== [2] ASSISTANT TEXT ===
I'll work this out properly. First, a key assumption: "30 feet from the battery" I'm reading as **one-way** distance, so the current travels 60 ft of wire total (out and back) — that's what sets the drop. Let me pull the real resistance figures and compute drops rather than guess.
=== [3] TOOL CALL: wiring_calc (call_9glenm5e) ===
{
"calculation": "awg_properties",
"awg": 4
}
=== [4] TOOL CALL: wiring_calc (call_fzbsrz57) ===
{
"calculation": "awg_properties",
"awg": 6
}
=== [5] TOOL CALL: wiring_calc (call_onbq2r8i) ===
{
"calculation": "awg_properties",
"awg": 8
}
=== [6] TOOL CALL: wiring_calc (call_3ptx8avw) ===
{
"calculation": "awg_properties",
"awg": 10
}
=== [7] TOOL RESULT: wiring_calc (call_9glenm5e) ===
# 4 AWG
Diameter: 5.189 mm (204.3 mil)
Cross-section: 21.1506 mm²
Resistance (copper): 0.815 Ω/km (0.00025 Ω/ft)
Current rating, chassis/free-air wiring: 135 A
Current rating, power transmission: 60 A
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
60 C 75 C 90 C
copper 70 A 85 A 95 A
aluminium 80 A 100 A 115 A
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
PVC/aluminium conduit: R 1.020 Ω/km, X 0.157 Ω/km
steel conduit: R 1.020 Ω/km, X 0.197 Ω/km
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
**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_fzbsrz57) ===
# 6 AWG
Diameter: 4.115 mm (162.0 mil)
Cross-section: 13.3018 mm²
Resistance (copper): 1.296 Ω/km (0.00040 Ω/ft)
Current rating, chassis/free-air wiring: 101 A
Current rating, power transmission: 37 A
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
60 C 75 C 90 C
copper 55 A 65 A 75 A
aluminium 60 A 75 A 85 A
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
PVC/aluminium conduit: R 1.610 Ω/km, X 0.167 Ω/km
steel conduit: R 1.610 Ω/km, X 0.210 Ω/km
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
**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.
=== [9] TOOL RESULT: wiring_calc (call_onbq2r8i) ===
# 8 AWG
Diameter: 3.264 mm (128.5 mil)
Cross-section: 8.3656 mm²
Resistance (copper): 2.061 Ω/km (0.00063 Ω/ft)
Current rating, chassis/free-air wiring: 73 A
Current rating, power transmission: 24 A
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
60 C 75 C 90 C
copper 40 A 50 A 55 A
aluminium 45 A 55 A 60 A
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
PVC/aluminium conduit: R 2.560 Ω/km, X 0.171 Ω/km
steel conduit: R 2.560 Ω/km, X 0.213 Ω/km
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
**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.
=== [10] TOOL RESULT: wiring_calc (call_3ptx8avw) ===
# 10 AWG
Diameter: 2.588 mm (101.9 mil)
Cross-section: 5.2612 mm²
Resistance (copper): 3.277 Ω/km (0.00100 Ω/ft)
Current rating, chassis/free-air wiring: 55 A
Current rating, power transmission: 15 A
The two figures differ because power transmission assumes bundled cable in a conduit where heat cannot escape, so it is far more conservative.
NEC Table 310.16 allowable ampacity (<=3 current-carrying conductors, 30 C ambient):
60 C 75 C 90 C
copper 30 A 35 A 40 A
aluminium 35 A 40 A 45 A
Use the column matching the **termination** rating, not the insulation: NEC 110.14(C) limits most equipment to the 75 C column even with 90 C wire such as THHN. Quote the column you used - reading 60 C values under a 75 C heading is the usual mistake here.
NEC 240.4(D) also caps overcurrent protection for 10 AWG at 30 A regardless of the ampacity above.
These are 30 C ambient with no bundling. Correct for ambient (310.15(B)(1)) and for more than three conductors (310.15(C)(1)) before using them.
AC values from NEC Ch.9 Table 9 (75 °C, 60 Hz, 3 single conductors in conduit):
PVC/aluminium conduit: R 3.900 Ω/km, X 0.164 Ω/km
steel conduit: R 3.900 Ω/km, X 0.207 Ω/km
**Do not work the AC drop out by hand from these.** Call this tool again with calculation=three_phase_drop (awg, length, current, voltage, power_factor, conduit) and it returns the drop, the percentage and the voltage at the load.
Hand-worked three-phase drops are wrong more often than they are right: the √3 factor gets written into the formula and then left out of the multiplication, which understates the answer by 1.73x and turns a marginal feeder into a passing one.
**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.
=== [11] THINKING ===
Now I have resistance per foot:
- 4 AWG: 0.00025 Ω/ft
- 6 AWG: 0.00040 Ω/ft
- 8 AWG: 0.00063 Ω/ft
- 10 AWG: 0.00100 Ω/ft
Now let me compute the DC voltage drop. The user is on DC, so I use the voltage_drop calculation (DC). Let me run voltage_drop for 4, 6, 8, 10 with length (one-way) = 9.144 m (30 ft), current 20A, voltage 12V.
Wait, but I need to check whether the tool interprets length as one-way and doubles it, or expects total. The description says "One-way cable length in metres." So it should double internally. Let me run and verify.
Let me run voltage_drop for 4, 6, 8, 10.
=== [12] TOOL CALL: wiring_calc (call_h51jldd7) ===
{
"awg": 4,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [13] TOOL CALL: wiring_calc (call_702gbikj) ===
{
"awg": 6,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [14] TOOL CALL: wiring_calc (call_4g9t0saf) ===
{
"awg": 8,
"calculation": "voltage_drop",
"current": "20",
"length": "9.144",
"voltage": "12"
}
=== [15] TOOL RESULT: wiring_calc (call_h51jldd7) ===
# 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.
=== [16] TOOL RESULT: wiring_calc (call_702gbikj) ===
# Voltage drop over 9.144 m of 6 AWG
**Drop: 474 mV** (round trip, 18.288 m of conductor)
Conductor: 6 AWG = 13.30 mm² (4.12 mm diameter), 1.296 Ω/km
Loop resistance: 23.7 mΩ
Power lost as heat: 9.481 W
That is 3.95% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
Voltage at the load: 11.53 V
## Nearby gauges, same run
- 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%
- 7 AWG ( 10.55 mm²): 597.8 mV = 4.98%
- 8 AWG ( 8.37 mm²): 753.8 mV = 6.28%
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
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] TOOL RESULT: wiring_calc (call_4g9t0saf) ===
# Voltage drop over 9.144 m of 8 AWG
**Drop: 753.8 mV** (round trip, 18.288 m of conductor)
Conductor: 8 AWG = 8.37 mm² (3.26 mm diameter), 2.061 Ω/km
Loop resistance: 37.69 mΩ
Power lost as heat: 15.08 W
That is 6.28% of a 12 V supply — above the usual 3% guideline — consider thicker wire or a shorter run.
Voltage at the load: 11.25 V
## Nearby gauges, same run
- 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%
- 9 AWG ( 6.63 mm²): 950.5 mV = 7.92%
- 10 AWG ( 5.26 mm²): 1.199 V = 9.99%
- 11 AWG ( 4.17 mm²): 1.511 V = 12.59%
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.
=== [18] THINKING (8s) ===
The tool confirms my hand calculation:
- 4 AWG: 298.1 mV = 2.48% ✓ under 3%
- 6 AWG: 474 mV = 3.95% ✗ over 3%
- 8 AWG: 753.8 mV = 6.28% ✗
So the answer is 4 AWG (which passes at 2.48%), and the next size smaller (6 AWG) fails at 3.95%.
Note: 5 AWG would be 3.13%, also over 3%. So 4 AWG is the smallest standard gauge that passes. Good.
The tool's voltage_drop uses round trip automatically (it doubled the length to 18.288 m).
Now let me write a clear answer. I'll state the assumption (30 ft one-way, so 60 ft round trip), give the pick (4 AWG), show its drop (298 mV, 2.48%, load sees 11.70V), and the next smaller (6 AWG, 474 mV, 3.95%, load sees 11.53V). Also note 5 AWG at 3.13% also fails. Mention ampacity is fine (20A well within all these). Note heat loss.
Let me present this cleanly.
=== [19] ASSISTANT TEXT ===
**Pick: 4 AWG copper.** At 30 ft one‑way (60 ft / 18.29 m round trip) it drops **298 mV = 2.48%** — under your 3% limit, with the load seeing about **11.70 V**.
Here's the margin you asked for:
| Gauge | Round‑trip loop R | Drop @ 20 A | % of 12 V | Load sees | Pass? |
|-------|------------------|-------------|-----------|-----------|-------|
| **4 AWG** (chosen) | 14.9 mΩ | **298 mV** | **2.48%** | 11.70 V | ✅ |
| **6 AWG** (next smaller) | 23.7 mΩ | **474 mV** | **3.95%** | 11.53 V | ❌ |
So the step down from 4 to 6 AWG costs you ~1.5× the drop and pushes you over the line. (For completeness, 5 AWG lands at 376 mV / 3.13% — also a fail, so 4 AWG is the smallest standard size that clears 3%. 8 AWG would be 754 mV / 6.28%.)
A few things worth knowing before you buy wire:
- **The math assumes 30 ft one way.** If "30 feet" was meant as the total round‑trip length, then 6 AWG would actually clear it (~1.98%) — but I've sized it for the worst case.
- **Ampacity is not your constraint here.** 20 A is well inside every gauge's rating (even 10 AWG is rated 30 A), so this is purely a voltage‑drop decision.
- **Heat in the wire:** 4 AWG dissipates ~6 W, 6 AWG ~9.5 W over the run. Not dangerous, but it's why the load voltage sags.
- **Battery sag under load:** a real 12 V battery isn't exactly 12.0 V under 20 A of load — if the system is marginal (e.g., starting an engine or running a compressor), consider 2 AWG (~1.56%) for extra headroom, since the drop scales linearly with current and any momentary surge will eat into your margin.
- These are free‑air copper figures; derate if the cable runs hot, bundled, or through conduit for long stretches.
Rule of thumb if you want to check other loads yourself: **Drop ≈ 2 × L(ft) × I(A) × R(Ω/ft)**, where the factor of 2 accounts for the return path.
=== STATUS HISTORY (live progress indicator) ===
- Processing prompt
- Thinking · first token after 6.2 s
- Thought: The user wants a wire gauge calculation for 12V DC, 20A load, 30 feet. Voltage drop < … Let me run awg_properties for 4, 6, 8, 10 in parallel first.
- Writing response
- Calling wiring_calc
- Calling wiring_calc
- Calling wiring_calc
- Calling wiring_calc
- Thinking
- Thought: Now I have resistance per foot: - 4 AWG: 0.00025 Ω/ft - 6 AWG: 0.00040 Ω/ft - 8 AWG: … Let me run and verify. Let me run voltage_drop for 4, 6, 8, 10.
- Calling wiring_calc
- Calling wiring_calc
- Calling wiring_calc
- Thinking
- Thought: The tool confirms my hand calculation: - 4 AWG: 298.1 mV = 2.48% ✓ under 3% - 6 AWG: … within all these). Note heat loss. Let me present this cleanly.
- Writing response
- Done · 7 tool calls · prefill 6.0 s for 12,871 tokens · 2,781 generated