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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.

Calculation mode

Use DC or RMS current for I²R loss.

Physical source-to-load distance; loop length is doubled internally.

Wire size input

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 FormulaRsingle = ρL/A.
Loop Resistance FormulaRloop = 2ρL/A for two equal conductors.
One-Way Length ConventionL is physical source-to-load cable length.
Total Conductor Length ConventionLtotal = 2 × Lone-way.
Voltage Drop FormulaVdrop = I × Rloop.
Total Wire Power Loss FormulaPloss,total = I²Rloop.
Per-Conductor Power Loss FormulaPsingle = I²Rsingle.
I²R / IVdrop IdentityI²Rloop equals I × Vdrop.
Energy Loss FormulaEloss = Ploss × t.
Wh / Joule Conversion1Wh = 3600J; 1kWh = 3.6e6J.
Loss Percentage DefinitionWire loss percentage is Ploss/Psource, equivalent to Vdrop/Vsupply for I > 0.
Load Voltage FormulaVload = Vsupply - Vdrop.
Source Power FormulaPsource = Vsupply × I.
Load Power FormulaPload = Vload × I when Vdrop < Vsupply.
Power Balance IdentityPsource = Pload + Ploss.
Wire Efficiency Definitionηwire = Pload/Psource × 100%, not system efficiency.
Zero Current PolicyI = 0 is valid and produces zero drop, zero loss, and no NaN percentage.
Negative Load Voltage PolicyLoad power and efficiency are withheld when conductor drop equals or exceeds supply voltage.
AWG Dataset ReuseAWG input uses data/reference/awg.ts.
AWG Precision PolicyRaw AWG area is used internally.
Material Data ReuseCopper/aluminum/custom resistivity reuse Wires infrastructure.
Reference Temperature PolicyPreset resistivity is a reference value near 20°C.
Temperature Correction BoundaryNo R(T) correction; WIR-011 owns that scope.
Temperature Rise BoundaryPower loss is not converted into wire temperature rise.
Ampacity BoundaryNo safe current or code ampacity result.
DC / AC BoundaryDC and low-frequency resistive conductor model only.
Three-Phase BoundaryNo partial three-phase cable-loss shortcut.
Motor BoundaryNo motor winding copper-loss model.
Transformer BoundaryNo transformer winding-loss model.
PCB BoundaryNo PCB trace-loss model.
Connector Resistance BoundaryConnector/contact resistance is excluded unless included in known loop resistance.
Source Resistance BoundaryBattery/source internal resistance is excluded.

Worked Examples

CaseCalculationResult
Baseline Rsingle1.724e-8 × 10 / 2.5e-60.06896Ω
Baseline Rloop2 × 0.06896Ω0.13792Ω
Voltage drop10A × 0.13792Ω1.3792V
Loss per conductor10² × 0.06896Ω6.896W
Total loop loss10² × 0.13792Ω13.792W
I²R identity10² × 0.13792Ω13.792W
IVdrop identity10 × 1.3792V13.792W
Two conductors2 × 6.896W13.792W
2 hour energy13.792W × 2h27.584Wh
Energy kWh27.584Wh / 10000.027584kWh
Energy joules27.584Wh × 360099302.4J
Source power12V × 10A120W
Load voltage12V - 1.3792V10.6208V
Load power10.6208V × 10A106.208W
Power balance106.208W + 13.792W120W
Loss percentage13.792 / 120 × 10011.49333%
Wire efficiency100 - 11.4933388.50667%
Double current(2I)²R4× loss
Double lengthRloop ×22× loss
Double areaRloop ÷21/2 loss
Double resistivityRloop ×22× loss
Zero currentI=00W loss
Zero lengthL=00Ω and 0W
Known loop R10² × 0.13792Ω13.792W
Known voltage drop10A × 1.3792V13.792W

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.

Wire Resistance Calculator

Available

Calculate conductor and loop resistance from material, length, area, and AWG.

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Wire Voltage Drop Calculator

Available

Calculate cable voltage drop and load voltage from known wire geometry.

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Wire Size Calculator

Available

Solve required conductor area from a voltage-drop limit.

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Maximum Wire Length Calculator

Available

Solve maximum one-way length for a known wire size and voltage-drop limit.

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AWG to mm² Converter

Available

Convert AWG to diameter, area, circular mils, and reference values.

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Documentation

Guides and lookup references linked to this tool.