Wire Power Loss Calculator
Calculate DC wire I²R power loss, voltage drop, energy loss, load power, and conductor delivery efficiency from wire resistance, length, area, AWG, and current. Results describe conductor loss only and do not verify temperature rise, ampacity, NEC compliance, or IEC compliance.
Engineering tool
Wire Power Loss Calculator
Calculate DC cable I²R conductor loss, voltage drop, optional energy loss, and wire delivery efficiency. This is not a wire temperature-rise, ampacity, or code-compliance calculator.
Use DC or RMS current for I²R loss.
Physical source-to-load distance; loop length is doubled internally.
Conductor metal area, not cable outer diameter.
Used for loss percentage and conductor delivery efficiency.
Energy loss equals power loss multiplied by time.
Result console
- Total Loop Wire Power Loss
- 13.792W
- Power Loss per Conductor
- 6.896W
- Wire Voltage Drop
- 1.3792V
- Loop Resistance
- 0.13792Ω
- Single-Conductor Resistance
- 0.06896Ω
- Energy Loss
- 27.584Wh
- Loss Percentage of Source Power
- 11.49333%
- Wire Delivery Efficiency
- 88.50667%
- Load Voltage
- 10.6208V
- Load Power
- 106.208W
- Source Power
- 120W
- One-Way Cable Length
- 10m
- Total Conductor Length
- 20m
- Wire Area
- 2.5mm²
- Material
- Copper
- Load Current
- 10A
Wire power loss is conductor I²R loss only. It does not verify ampacity, wire temperature rise, insulation rating, installation method, connector heating, source resistance, or electrical-code compliance.
Formula reference
Wire power loss formulas
WIR-005 keeps the primary intent on DC wire/cable I²R conductor loss and uses the same loop convention as WIR-001 through WIR-004.
Rsingle = ρL/ARloop = 2ρL/AVdrop = I × RloopPloss = I²RloopPloss = I × VdropEloss = Ploss × tPsource = Vsupply × IVload = Vsupply - VdropPload = Vload × Iηwire = Pload/Psource × 100%Variable definitions
- ρ
- conductor resistivity
- L
- one-way cable length
- A
- conductor cross-sectional area
- I
- conductor current
- ηwire
- conductor delivery efficiency, not system efficiency
WIR-005 Formula Audit
| Single-Conductor Resistance Formula | Rsingle = ρL/A. |
|---|---|
| Loop Resistance Formula | Rloop = 2ρL/A for two equal conductors. |
| One-Way Length Convention | L is physical source-to-load cable length. |
| Total Conductor Length Convention | Ltotal = 2 × Lone-way. |
| Voltage Drop Formula | Vdrop = I × Rloop. |
| Total Wire Power Loss Formula | Ploss,total = I²Rloop. |
| Per-Conductor Power Loss Formula | Psingle = I²Rsingle. |
| I²R / IVdrop Identity | I²Rloop equals I × Vdrop. |
| Energy Loss Formula | Eloss = Ploss × t. |
| Wh / Joule Conversion | 1Wh = 3600J; 1kWh = 3.6e6J. |
| Loss Percentage Definition | Wire loss percentage is Ploss/Psource, equivalent to Vdrop/Vsupply for I > 0. |
| Load Voltage Formula | Vload = Vsupply - Vdrop. |
| Source Power Formula | Psource = Vsupply × I. |
| Load Power Formula | Pload = Vload × I when Vdrop < Vsupply. |
| Power Balance Identity | Psource = Pload + Ploss. |
| Wire Efficiency Definition | ηwire = Pload/Psource × 100%, not system efficiency. |
| Zero Current Policy | I = 0 is valid and produces zero drop, zero loss, and no NaN percentage. |
| Negative Load Voltage Policy | Load power and efficiency are withheld when conductor drop equals or exceeds supply voltage. |
| AWG Dataset Reuse | AWG input uses data/reference/awg.ts. |
| AWG Precision Policy | Raw AWG area is used internally. |
| Material Data Reuse | Copper/aluminum/custom resistivity reuse Wires infrastructure. |
| Reference Temperature Policy | Preset resistivity is a reference value near 20°C. |
| Temperature Correction Boundary | No R(T) correction; WIR-011 owns that scope. |
| Temperature Rise Boundary | Power loss is not converted into wire temperature rise. |
| Ampacity Boundary | No safe current or code ampacity result. |
| DC / AC Boundary | DC and low-frequency resistive conductor model only. |
| Three-Phase Boundary | No partial three-phase cable-loss shortcut. |
| Motor Boundary | No motor winding copper-loss model. |
| Transformer Boundary | No transformer winding-loss model. |
| PCB Boundary | No PCB trace-loss model. |
| Connector Resistance Boundary | Connector/contact resistance is excluded unless included in known loop resistance. |
| Source Resistance Boundary | Battery/source internal resistance is excluded. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| Baseline Rsingle | 1.724e-8 × 10 / 2.5e-6 | 0.06896Ω |
| Baseline Rloop | 2 × 0.06896Ω | 0.13792Ω |
| Voltage drop | 10A × 0.13792Ω | 1.3792V |
| Loss per conductor | 10² × 0.06896Ω | 6.896W |
| Total loop loss | 10² × 0.13792Ω | 13.792W |
| I²R identity | 10² × 0.13792Ω | 13.792W |
| IVdrop identity | 10 × 1.3792V | 13.792W |
| Two conductors | 2 × 6.896W | 13.792W |
| 2 hour energy | 13.792W × 2h | 27.584Wh |
| Energy kWh | 27.584Wh / 1000 | 0.027584kWh |
| Energy joules | 27.584Wh × 3600 | 99302.4J |
| Source power | 12V × 10A | 120W |
| Load voltage | 12V - 1.3792V | 10.6208V |
| Load power | 10.6208V × 10A | 106.208W |
| Power balance | 106.208W + 13.792W | 120W |
| Loss percentage | 13.792 / 120 × 100 | 11.49333% |
| Wire efficiency | 100 - 11.49333 | 88.50667% |
| Double current | (2I)²R | 4× loss |
| Double length | Rloop ×2 | 2× loss |
| Double area | Rloop ÷2 | 1/2 loss |
| Double resistivity | Rloop ×2 | 2× loss |
| Zero current | I=0 | 0W loss |
| Zero length | L=0 | 0Ω and 0W |
| Known loop R | 10² × 0.13792Ω | 13.792W |
| Known voltage drop | 10A × 1.3792V | 13.792W |
Engineering Notes
- Wire power loss is electrical conductor heating power.
- Total loop wire power loss includes the outgoing and return conductors.
- Power loss per conductor is half the total only when the two conductors are equal.
- Loop resistance must not be doubled again in known loop resistance mode.
- Voltage drop and power loss are linked by Ploss = I × Vdrop.
- Current is squared in I²R loss, so current margin matters.
- Energy loss is power loss accumulated over operating time.
- Watts and watt-hours are different quantities.
- Copper usually dissipates less power than aluminum for the same area.
- Reference resistivity does not include hot conductor resistance.
- This calculator does not calculate wire temperature rise.
- This calculator does not check ampacity or electrical-code compliance.
- Connector and terminal losses are excluded unless included in a known loop resistance.
- Battery/source internal resistance is outside this wire-loss model.
Common Mistakes
- Using single-conductor resistance instead of loop resistance.
- Doubling loop resistance twice.
- Entering loop length as one-way length.
- Forgetting the return conductor.
- Using I × R as power instead of I²R.
- Forgetting that current is squared.
- Confusing voltage drop with power loss.
- Confusing power with energy.
- Mixing W and Wh.
- Mixing Wh and kWh.
- Mixing mΩ and Ω.
- Mixing mA and A.
- Using rounded AWG display area internally.
- Assuming power loss directly gives wire temperature.
- Assuming low power loss proves safe ampacity.
- Including connector resistance without intending to.
- Using DC resistance as exact high-frequency AC resistance.
Support reference
FAQ
How do I calculate wire power loss?
Calculate loop resistance for the complete source-load-return path, then use Ploss = I²Rloop. The same loss also equals I × Vdrop.
What is the I²R loss formula?
I²R loss is P = I²R, where I is conductor current and R is the resistance carrying that current.
Why is current squared in wire power loss?
Resistive power loss rises with the square of current. Doubling current through the same loop resistance produces four times the heat-producing loss.
How do I calculate cable power loss?
For a two-conductor DC cable, compute Rsingle = ρL/A, Rloop = 2Rsingle, and Ploss = I²Rloop.
How do I calculate wire resistance before power loss?
Use R = ρL/A for one conductor. For a source-and-return DC cable pair, use Rloop = 2ρL/A.
Why is the return conductor included?
Current flows through the outgoing conductor and returns through another conductor, so both conductors dissipate power.
What is the difference between single-conductor and loop loss?
Single-conductor loss is I²Rsingle. Total loop wire loss is the combined loss in the outgoing and return conductors.
How does current affect wire loss?
Wire power loss scales with current squared. A small current increase can cause a much larger loss increase.
How does wire length affect power loss?
At fixed current, material, and area, doubling one-way length doubles loop resistance and doubles total wire loss.
How does wire size affect power loss?
A larger conductor area reduces resistance and lowers I²R loss for the same length and current.
How does AWG affect wire power loss?
Lower AWG numbers generally mean larger conductors, lower resistance, less voltage drop, and less I²R loss.
How does copper compare with aluminum?
Copper has lower resistivity than aluminum, so the same area and length usually dissipate less power in copper.
How do I calculate wire voltage drop from power loss?
If current is known and nonzero, Vdrop = Ploss / I. The calculator also computes Vdrop directly from I × Rloop.
Why is P=I²R equal to P=IVdrop?
Because Vdrop = IR. Substituting IR for voltage in P = IV gives P = I²R.
How do I calculate energy lost in a cable?
Energy loss is Eloss = Ploss × time. The calculator reports joules, watt-hours, and kilowatt-hours.
What is the difference between watts and watt-hours?
Watts measure power at an instant. Watt-hours measure energy accumulated over time.
How do I convert Wh to joules?
One watt-hour equals 3600 joules. One kilowatt-hour equals 3.6 million joules.
What is wire delivery efficiency?
Wire delivery efficiency is the load power after conductor drop divided by source electrical power in the simple DC conductor model.
Does this calculator calculate system efficiency?
No. It only estimates conductor delivery efficiency and excludes source, converter, switch, connector, and load efficiency.
Does wire temperature affect power loss?
Yes. Resistance changes with conductor temperature, so real I²R loss can differ from the reference-resistivity estimate.
Does this calculator calculate wire temperature rise?
No. It calculates electrical heating power, not conductor operating temperature or temperature rise.
Does this calculator check ampacity?
No. It does not verify safe current, ampacity tables, insulation rating, bundling, or installation method.
Can I use this calculator for AC?
Only as a simple low-frequency resistive estimate. Complete AC conductor loss may require RMS current, AC resistance, skin effect, proximity effect, and phase conditions.
Does connector resistance add additional power loss?
Yes. Connector and terminal resistance can add I²R loss, but this calculator does not include it unless you include it in a known loop resistance input.
What happens if wire voltage drop exceeds supply voltage?
The raw conductor loss is calculated, but load power and delivery efficiency are marked not physically meaningful under the simple source-and-wire model.
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