From power to current
I = P / (sqrt(3) x U x cos phi x eta) = 55000 / (1.732 x 400 x 0.86 x 0.94) = 98.2 A. Single-phase without sqrt(3); DC without cos phi: 15000 / (220 x 0.88) = 77.48 A. The figures are examples from a nameplate.
Reference tool — arithmetic, not motor data
Motor current.
Current · input power · kVA · kvar · starting current
Power, volts, amps.
Type a line (55 kW 400 V cos 0.86 eff 94 %; single-phase 2.2 kW 230 V cos 0.8 eff 82 %; for the power, 102 A 400 V cos 0.86 eff 94 %; add IA/IN 7.2 for the starting current) or fill in the fields: the line and the fields stay in step.
Examples:
All 130 engineering tools
Enter the rated power of an electric motor from its nameplate, in kW, hp or PS, the voltage, cos phi and the efficiency, and the calculator gives the full-load line current of a three-phase, single-phase or DC motor, the electrical input power, the apparent power in kVA and the reactive power in kvar. It also works the other way, the shaft power from a measured or nameplate current, and with the starting current ratio IA/IN it gives the starting current, direct-on-line or star-delta. The working is shown with your numbers, the power triangle is drawn to scale, and the result is a line you can copy.
Arithmetic only: no typical cos phi, efficiency or IA/IN, and no cable or protection sizing. The nameplate and the motor maker data govern.
How it is worked out
Current, power, start.
Input, kVA and kvar
P_in = P / eta = 55 / 0.94 = 58.51 kW. S = sqrt(3) x U x I = 68.04 kVA. Q = sqrt(S^2 - P_in^2) = 34.72 kvar. Back from a current: P = sqrt(3) x U x I x cos phi x eta, so 102 A gives 57.13 kW.
Starting current
I_start = IA/IN x I = 7.2 x 98.2 = 707 A direct-on-line, with the ratio from the nameplate (7.2 is an example). Star-delta: one third in the line, 235.7 A.
| Voltage, V | DC or single-phase, A per kW | Three-phase, A per kW |
|---|---|---|
| 110 | 9.091 | 5.249 |
| 220 | 4.545 | 2.624 |
| 230 | 4.348 | 2.510 |
| 400 | 2.500 | 1.443 |
| 440 | 2.273 | 1.312 |
| 690 | 1.449 | 0.837 |
The voltages are round supply voltages, not motor data. Example: 58.51 kW of input at 400 V three-phase and cos phi 0.86 is 58.51 x 1.443 / 0.86 = 98.2 A.
Sources
The current is plain arithmetic: I = P / (sqrt(3) x U x cos phi x eta) on three-phase, P / (U x cos phi x eta) on single-phase and P / (U x eta) on DC, P_in = P / eta, S = sqrt(3) x U x I, Q = sqrt(S^2 - P_in^2), and the reverse. That the rated output of a motor is the mechanical power at the shaft is stated in IEC 60034-1. The formula with the shaft power and the nameplate cos phi and efficiency is given alike by two motor references, and a maker data sheet of a 110 kW 400 V motor gives a rated current within 0.5 A of it. IA/IN is the ratio of the locked-rotor current to the rated current, as motor data sheets define it. That star-delta starting takes one third of the direct-on-line starting current from the line is stated in the starter data of two makers, for a motor whose delta voltage is the supply voltage. 1 hp = 745.69987 W (550 ft lbf/s) and 1 PS = 735.49875 W (75 kgf m/s) are exact by definition. The motor nameplate and the maker data always come first.
Before you work it out
Questions about motor current
How is the current of a three-phase motor worked out?
Divide the rated power from the nameplate by sqrt(3) (1.732), the voltage between the phases, cos phi and the efficiency: I = P / (sqrt(3) x U x cos phi x eta). For a motor of 55 kW at 400 V with cos phi 0.86 and an efficiency of 94 % (example figures from a nameplate, not typical ones): 55000 / (1.732 x 400 x 0.86 x 0.94) = 98.2 A. The rated current on the nameplate of your motor comes first; the working shows how the figures fit together.
And for a single-phase or a DC motor?
Single-phase: I = P / (U x cos phi x eta), so 2.2 kW at 230 V, cos phi 0.8 and 82 % gives 2200 / (230 x 0.8 x 0.82) = 14.58 A. DC has no cos phi: I = P / (U x eta), so 15 kW at 220 V and 88 % gives 15000 / (220 x 0.88) = 77.48 A. The figures are examples; take them from the nameplate of the motor in question.
Is the power on the nameplate the shaft power or the electrical input?
On a motor nameplate the rated output is the mechanical power at the shaft. The electrical input is larger by the losses: P_in = P / eta, 55 / 0.94 = 58.51 kW, so 3.51 kW of losses. If the figure you have is the electrical input, switch the calculator to the electrical input: then I = P_in / (sqrt(3) x U x cos phi), and the efficiency is needed only for the shaft power.
What are the kVA and the kvar?
The apparent power S = sqrt(3) x U x I, here 1.73205 x 400 x 98.201 / 1000 = 68.036 kVA, which is also the input power divided by cos phi (58.511 / 0.86). The reactive power is the third side of the power triangle: Q = sqrt(S^2 - P_in^2) = sqrt(68.036^2 - 58.511^2) = 34.72 kvar. Rounded figures put into the square root change the last digit, so the working on the page keeps three decimals. On DC there is no apparent or reactive power.
How is the starting current worked out?
Multiply the rated current by the starting current ratio IA/IN from the nameplate or the maker data sheet: at IA/IN 7.2 (an example), 7.2 x 98.2 = 707 A direct-on-line. No typical ratio is put in. With star-delta starting, the line current at the start is one third of the direct-on-line starting current, 707 / 3 = 235.7 A, as two starter makers give it, for a motor whose delta voltage is the supply voltage; the peak at the switch from star to delta is not worked out.
Which units does the calculator take, and how is the cable chosen?
The power in kW, W, MW, hp (mechanical horsepower, 745.69987 W) or PS (metric horsepower, 735.49875 W); the voltage in V or kV; the current in A; cos phi as a fraction from 0 to 1; the efficiency as 94, 94 % or 0.94. A frequency written in the line goes into the result line and not into the arithmetic. The cable and its protection are chosen to the class society rules and the maker data; this page gives no sizing figures.
Parts for the motor or its starter?
Send the motor type and the part.
The calculator works out the current from the figures you enter. When bearings, a fan, a terminal box, a contactor or a whole motor is needed, send the motor type, its serial number and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
Buyer tools
