Calculator
3 columns on large screens, 2 on smaller, 1 on mobile.Example Data Table
These are sample scenarios to help you sanity-check outputs.
| Scenario | Vs (V) | Duty (%) | Ra (Ω) | Ia (A) | Brush (V) | Ke (V/rad/s) | Estimated rpm |
|---|---|---|---|---|---|---|---|
| 24V PM motor, moderate load | 24 | 100 | 0.30 | 8 | 1 | 0.030 | ~6,550 |
| 12V motor with PWM limit | 12 | 60 | 0.45 | 3 | 0.5 | 0.025 | ~2,600 |
| Higher resistance wiring added | 24 | 100 | 0.30 | 10 | 1 | 0.030 | ~5,100 |
Formula Used
- Effective voltage: Veff = Vsupply × (duty/100)
- Back EMF: E = Veff − Ia(Ra + Rextra) − Vbrush
- Speed using Ke: ω = E / Ke, rpm = ω × 60 / (2π)
- Machine EMF: E = (P·Φ·Z·N) / (60·A) ⇒ N = (60·A·E) / (P·Φ·Z)
- Torque (machine): T ≈ (P·Z·Φ·Ia) / (2π·A)
- Torque (SI Ke): T ≈ Ke · Ia
- Output speed with gears: rpmshaft = rpmmotor / gear ratio
How to Use This Calculator
- Pick motor type and choose a speed method.
- Enter supply voltage and PWM duty, if used.
- Fill resistance and brush drop to model voltage loss.
- Provide armature current or switch to load torque mode.
- Add gear ratio and wheel diameter for output motion.
- Press Submit to view results above the form.
- Use CSV or PDF buttons to save outputs.
FAQs
1) Which method should I choose?
Use Ke if your datasheet lists it, because it already captures the motor’s magnetic design. Use machine constants when you know poles, conductors, paths, and flux, such as in educational or detailed machine models.
2) Why does speed drop under load?
Load increases armature current, which increases voltage drop across resistances and reduces back EMF. Since speed is proportional to back EMF, the operating rpm falls as current rises.
3) What does brush drop represent?
Brush drop approximates the voltage lost across brushes and commutator contact. It is often between 0.5–2.0 V depending on motor size and current.
4) How does PWM affect speed?
PWM changes the average applied voltage. This tool uses an effective voltage equal to supply times duty cycle, which is a practical approximation for many controllers and motor inductances.
5) Why is flux important in the machine method?
Flux links the electrical and mechanical sides of the motor. Higher flux raises torque per amp but reduces speed for the same back EMF, so flux sets the torque–speed tradeoff in DC machines.
6) How should I model a series motor?
For a series motor, flux increases with armature current until saturation. Use the series kf and, if available, a saturation flux value to prevent unrealistic flux at high currents.
7) Are the power and efficiency values exact?
They are approximate because real losses include temperature effects, iron losses, and controller switching losses. Add an estimate in mechanical losses to better match measured performance.
8) Can I use this for gear trains and wheels?
Yes. Enter a gear ratio and efficiency to estimate shaft speed and torque. If you also enter wheel diameter, the calculator estimates linear speed for quick motion checks.