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Power & current

Three-Phase & Single-Phase Current Calculator

Work out the current a load draws from its power rating. Choose three-phase or single-phase, say whether your voltage is line-to-line or line-to-neutral, and enter the power in kW, hp or kVA. The result shows each substitution so you can check it against your own working.

For estimation and education. Not a substitute for a licensed engineer, the applicable codes (IEC 60364, NEC/NFPA 70, BS 7671, local regulations) or manufacturer data. Read the disclaimer.

Supply system
The voltage I am entering is

Supply

V

Load

kW

0 < PF ≤ 1

1 if P is electrical input; motor η if P is shaft output.

Result

Line current — Engineerly. Estimate for education only; verify against applicable codes and manufacturer data.

Line current
180.4A
Apparent power
125kVA
Real input power
100kW
Reactive power
75kVAr
Line-to-line voltage
400V
Line-to-neutral voltage
230.94V

Working, with your numbers

  1. 1. Line current
    I = P / (√3 × V_LL × PF × η)
    I = 100,000 W / (1.73205 × 400 V × 0.8 × 1)
    = 180.42 A
  2. 2. Apparent power drawn
    S = P / (PF × η)
    S = 100 kW / (0.8 × 1)
    = 125 kVA

Assumptions

  • Balanced three-phase load with sinusoidal voltage and current.
  • PF is the displacement power factor of the load; harmonics are ignored.
  • η converts output power to electrical input power. Use η = 1 if P is already the electrical input.
System: Three-phase (line-to-line voltage)
Voltage: 400 V
Power: 100 kW
Power factor: 0.8
Efficiency: 1

Check before you rely on this

  • Motor nameplate full-load current (or the code's motor current tables) takes precedence over a calculated value for protective device and conductor selection.
  • Estimation and education only. Not a substitute for a licensed engineer, the applicable code (IEC 60364, NEC/NFPA 70, BS 7671 or local regulations) or manufacturer data.

How to use this calculator

  1. Select three-phase or single-phase. For three-phase, state whether the voltage you know is line-to-line (for example 400 V or 480 V) or line-to-neutral (230 V or 277 V).
  2. Choose the power unit. Use kW for real power, hp for a motor's rated shaft output, or kVA when you know the apparent power, as with transformers and generators.
  3. Enter the power factor. For kW and hp inputs also enter the efficiency: 1 when the figure is already electrical input, or the motor efficiency when it is shaft output.
  4. Read the current, then look at the working panel to see the formula with your values substituted.
  5. Copy the link to share the exact inputs, or print the result for a calculation file.

How it works: the formula

Three-phase, from real power: I = P / (√3 × V_LL × PF × η) Three-phase, from apparent power: I = S / (√3 × V_LL) Single-phase, from real power: I = P / (V × PF × η) Single-phase, from apparent power: I = S / V Line-to-neutral input: V_LL = √3 × V_LN

The √3 comes from the geometry of a balanced three-phase system. The voltage between two lines is √3 times the voltage from a line to neutral, and total power is three times the per-phase power: P = 3 × V_LN × I × PF = √3 × V_LL × I × PF. Rearranging that gives the current.

Variables and units

SymbolMeaningUnit
ILine currentA
PReal (active) power: output power if η < 1, input power if η = 1W
SApparent powerVA
V_LLLine-to-line voltageV
V_LNLine-to-neutral (phase) voltageV
PFPower factor, cos φ (0 < PF ≤ 1)—
ηEfficiency, output ÷ input (0 < η ≤ 1)—

Worked example

A 100 kW three-phase load on a 400 V supply at power factor 0.8, with P taken as electrical input (η = 1):

I = 100 000 W / (1.73205 × 400 V × 0.8 × 1) = 100 000 / 554.26 = 180.42 A

For a 500 kVA transformer secondary at 415 V, the full-load current is 500 000 / (1.73205 × 415) = 695.60 A. If the same 100 kW load were described by its 230 V line-to-neutral voltage, V_LL = 1.73205 × 230 = 398.37 V and the current is 181.16 A. The small difference comes from 230 V × √3 being slightly less than 400 V.

Assumptions

  • Three-phase loads are balanced, so every line carries the same current.
  • Voltages and currents are sinusoidal. PF is the displacement power factor.
  • When you enter hp, P is the motor's shaft output, converted at 1 hp = 745.7 W.

Limitations

  • Real motor current at a given load depends on the motor's design. For protective devices and conductors, use the nameplate full-load current, or the motor current tables in your code (NEC Article 430 tables, for example) where they apply.
  • Unbalanced three-phase loads need each phase worked out separately.
  • Harmonic currents from electronic loads raise RMS current above this sinusoidal estimate.
  • Starting (inrush) current is several times the running current and is not covered here.

References

Standards and texts that cover this topic. Use the edition adopted in your jurisdiction.

  • IEEE Std 141, Recommended Practice for Electric Power Distribution for Industrial Plants ("Red Book") — power and current relationships in three-phase systems.
  • IEC 60050-131 / IEC 60050-141, International Electrotechnical Vocabulary — definitions of active, reactive and apparent power and polyphase quantities.
  • NFPA 70, National Electrical Code, Article 430 — motor full-load current tables used for conductor and protection sizing in NEC jurisdictions.

Frequently asked questions

Why does three-phase current use √3 rather than 3?

Total three-phase power is 3 × V_LN × I × PF. Because V_LL = √3 × V_LN, the same power written with line-to-line voltage is √3 × V_LL × I × PF. With line-to-line voltage the factor is √3; with line-to-neutral voltage it is 3. This calculator converts for you when you choose line-to-neutral.

Should I use efficiency for a motor?

Yes, when the power you have is the rated shaft output, which is what a nameplate kW or hp figure normally is. The motor takes more electrical power than it delivers, so divide by efficiency. If you measured electrical input power with a meter, leave efficiency at 1.

Why does the kVA input ignore power factor?

Apparent power already includes the effect of power factor: S = V × I for single-phase and √3 × V_LL × I for three-phase. Power factor only matters when you start from real power. Here it is used only to split the kVA into kW and kVAr.

Is 400 V the same as 230 V three-phase?

On a 230/400 V system, 230 V is the line-to-neutral voltage and 400 V is the line-to-line voltage of the same supply. Pick the selector that matches the number you enter. Getting this wrong changes the current by a factor of √3.

Can I use this to choose a breaker size?

Only as a starting point. Breaker and conductor sizing must follow your installation code. That means continuous-load factors, motor rules, grouping and ambient corrections, and the manufacturer's data.

Related calculators

  • kVA to kW Converter (and kVAr) — Convert between kVA, kW and kVAr using power factor, solve the power triangle from any two values and get the matching line current.
  • Cable Voltage Drop Calculator — Voltage drop for single-phase, three-phase and DC cables with temperature-corrected copper or aluminium resistance, reactance, % limit check and minimum size solver.
  • Generator Sizing Calculator — Size a generator set from a load table: running kW/kVA, diversity, motor starting kVA by DOL, soft starter or VFD, margin, derating and a common kVA rating.

How these formulas were checked: methodology and testing.