Calculate back EMF or terminal voltage from RPM with Kv or Ke motor constants, reverse-solve speed, and include armature voltage drop when known.
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Voltage from RPM Formula
The following formula is used to calculate the Voltage from RPM (rotational speed), torque, and current using an ideal power-balance assumption.
- Where V is the Voltage from RPM (volts)
- t is the torque (N·m)
- w is the rotational speed (RPM)
- I is the current (amps)
To calculate the voltage from RPM, multiply the torque by the RPM, divide by the current, then multiply by 2 times pi over 60 (which converts RPM to radians per second).
Important: This relationship comes from equating mechanical power Pmech = τ·ω to electrical power Pelec = V·I, which assumes ideal (100% efficient) conversion and DC electrical power. It does not represent a motor’s back-EMF/open-circuit generator voltage in general (those depend on machine constants, losses, and for AC, power factor and phase).
| RPM | Voltage (V) |
|---|---|
| 1 | 0.0314 |
| 5 | 0.1571 |
| 10 | 0.3142 |
| 30 | 0.9425 |
| 60 | 1.8850 |
| 100 | 3.1416 |
| 200 | 6.2832 |
| 300 | 9.4248 |
| 500 | 15.7080 |
| 600 | 18.8496 |
| 750 | 23.5619 |
| 1000 | 31.4159 |
| 1200 | 37.6991 |
| 1500 | 47.1239 |
| 1800 | 56.5487 |
| 2000 | 62.8319 |
| 2500 | 78.5398 |
| 3000 | 94.2478 |
| 3600 | 113.0973 |
| 5000 | 157.0796 |
| * Calculated using V = (2π/60) × t × RPM ÷ I with fixed example values t = 15 N·m and I = 50 A (so V ≈ 0.0314159 × RPM). | |
How to Calculate Voltage from RPM?
The following example problems outline how to calculate Voltage from RPM.
Example Problem #1
- First, determine the torque (N-m). In this example, the torque (N-m) is determined to be 15 .
- Next, determine the RPM. For this problem, the RPM is measured to be 4 .
- Next, determine the current (amps). In this case, the current (amps) is found to be 50.
- Finally, calculate the Voltage from RPM using the formula above:
V = 2π / 60 * t * w / I
Inserting the values from above and solving yields:
V = 2*3.14159/ 60 * 15 * 4 / 50 = .125 (volts)
Example Problem #2
Using the same method as above, determine the variables required by the formula. For this example problem, these are:
torque (N-m) = 41
RPM = 1
current (amps) = 52
Enter these given values into the calculator above yields:
V = 2*3.1415/ 60 * 41 * 1 / 52 = .082 (volts)
