Torque Calculator: Force, Radius and Power

Find the torque of a force on an arm, the force for a given torque, and the power that torque delivers at a speed.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Torque is the force times the perpendicular distance from the axis. If the force is not at right angles to the arm, only the part at right angles counts, so multiply by the sine of the angle.

Power is the torque times the angular speed. Enter the speed in rev/min and the calculator converts it to radians per second.

Formulas used

  • T = F\,r\sin\varphi
  • P = T\,\omega
  • \omega = \dfrac{2\pi N}{60}

Worked example

With the default numbers in the calculator above:

  1. Torque: 25.00 N·m
  2. Torque in other units: 2.55 kgf·m and 18.44 lbf·ft
  3. Angular speed: 157.08 rad/s
  4. Power at that speed: 3.93 kW (3926.99 W)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? The force, from the torque and the radius; Distance from the axis (arm length or radius) 250 mm; Angle between the force and the arm (90 = square on, the best) 60 °; Torque (used if you know it) 25 N·m.

  1. Force needed: 115.47 N
  2. Force in kilograms-force: 11.77 kg-force
  3. Torque in other units: 2.55 kgf·m and 18.44 lbf·ft
  4. Angular speed: 157.08 rad/s
  5. Power at that speed: 3.93 kW (3926.99 W)

Common questions

What is the unit of torque?

The newton metre (N·m). It is not the same as the joule, which is also a newton metre, because torque is a vector and energy is not.

Why does a longer spanner help?

The same torque needs less force when the arm is longer.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Standard physics and engineering texts (torque and power).

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