Shaft Power, Torque & Speed Calculator
Solve P = T·ω for shaft power, torque, or rotational speed. Enter any two values — get everything else, including efficiency losses, belt force, and design torque.
P = T·ω
SI & Imperial
Efficiency & losses
Belt force & speed
Safety factor
Free to use
Solve For
Quick Presets
Power, Torque & Speed
RPM
SI
Imperial
Key Results
Enter at least two values above and click Calculate.
All Values & Unit Conversions
—
Efficiency & Power Losses
Bearing, gear and belt losses — P_in = P_out / η
Design torque = T × Sf (typical: 1.25–2.0)
—
Belt, Pulley & Tangential Force
Enter a pulley radius to see belt force and speed results.
Formula Reference
| Solve For | Exact Formula | Convenient Shortcut | Notes |
|---|---|---|---|
| Power P | P = T × 2πn / 60 | P(kW) = T(N·m) × n / 9 550 | T in N·m, n in RPM → P in W |
| Torque T | T = P × 60 / (2πn) | T(N·m) = 9 550 × P(kW) / n | T(lbf·ft) = 5 252 × HP / n |
| Speed n | n = P × 60 / (2π × T) | n = 9 550 × P(kW) / T(N·m) | Result in RPM |
| Angular vel. ω | ω = 2πn / 60 | ω ≈ n × 0.10472 | Result in rad/s |
| Belt force F | F = T / r | — | T in N·m, r in m → F in N |
| Belt speed v | v = ω × r | v = π × d × n / 60 | r in m → v in m/s |
| Input power P_in | P_in = P_out / η | — | η as decimal (0–1) |
| Design torque T_d | T_d = T × Sf | — | Sf = service / safety factor |
Common Questions
What is the shaft power formula?
Shaft power is P = T × ω, where T is torque (N·m) and ω is angular velocity (rad/s). Substituting ω = 2πn/60 gives P = T × 2πn/60. Shortcuts: T(N·m) = 9 550 × P(kW)/n · T(lbf·ft) = 5 252 × HP/n.
How do I calculate torque from power and RPM?
Rearrange: T = P × 60 / (2πn). Shortcut: T(N·m) = 9 550 × P(kW) / n. Example — 5 kW at 1 450 RPM: T = 9 550 × 5 / 1 450 = 32.9 N·m.
How do I convert RPM to angular velocity?
ω (rad/s) = 2π × n / 60. Quick multiplier: ω ≈ n × 0.10472. Example: 1 500 RPM → 1 500 × 0.10472 = 157.08 rad/s.
What service factor value should I use?
Typical values: 1.0–1.25 for smooth, uniform load (fans, centrifugal pumps) · 1.25–1.75 for moderate shock (conveyors, compressors, mixers) · 1.75–2.5+ for heavy shock (stone crushers, punch presses, reciprocating pumps). Design torque = T × Sf.
Why does drivetrain efficiency matter for motor sizing?
Efficiency accounts for losses in bearings, gears, belts, and couplings. If you need 10 kW at the output shaft and the drivetrain is 90% efficient, the motor must supply 10 / 0.90 = 11.1 kW — 1.1 kW is lost to heat. Never size a motor based purely on the output requirement.