Calculate braking torque from mass, deceleration and radius, inertia and angular deceleration, or friction coefficient, normal force and radius.

Ideal torque from a tangential braking force: ฯ„ = mar. For a vehicle, use wheel rolling radius and the mass assigned to that wheelโ€”not brake rotor radius.

Positive or negative sets torque direction. Suggested magnitudes are 0.2g, 0.5g and 1g; they are not safety ratings.

Distance from rotation axis to the force line. Vehicle deceleration uses the wheel rolling radius.

Braking Torque Formula

Choose the method that matches your inputs. These are alternative ideal models, not torques to add together.

tau = mar, tau = Iฮฑ, tau = ฮผ Nr
  • ฯ„ is torque (Nยทm); its sign follows the chosen positive direction, except the friction method reports magnitude.
  • m is mass (kg), a is signed linear acceleration (m/sยฒ), and r is the perpendicular force lever arm (m).
  • I is moment of inertia (kgยทmยฒ) and ฮฑ is angular acceleration (rad/sยฒ). The speed-change method uses ฮฑ = (ฯ‰final โˆ’ ฯ‰initial) / t.
  • ฮผ is friction coefficient, N is normal force (N), and r is effective friction radius (m).

For vehicle deceleration, use wheel rolling radius and the mass assigned to that wheel, not rotor radius. Angular methods give net torque; other applied torques must be accounted for separately. For multiple friction interfaces, sum normal forces only when they share the same coefficient and effective radius. These estimates do not establish safe brake sizing.

How to Calculate Braking Torque?

The following example problems outline how to calculate Braking Torque.

Example Problem #1

  1. Select From mass and deceleration. Enter a mass of 1,000 kg.
  2. Enter signed linear acceleration of โˆ’4 m/sยฒ.
  3. Enter a perpendicular lever arm of 0.3 m.
  4. Select Calculate to find the corresponding torque: 

ฯ„ = mar

Inserting the values from above and solving yields: 

ฯ„ = 1,000 ร— (โˆ’4) ร— 0.3 = โˆ’1,200 Nยทm. The sign indicates direction; the magnitude is 1,200 Nยทm.

Example Problem #2

Select From inertia and angular acceleration for this example:

Moment of inertia = 5 kgยทmยฒ

Signed angular acceleration = โˆ’2 rad/sยฒ

Equivalently, angular velocity falls from 20 rad/s to zero in 10 s.

Select Calculate to obtain net torque: 

ฯ„ = Iฮฑ = 5 ร— (โˆ’2) = โˆ’10 Nยทm. In the friction method, ฮผ = 0.4, N = 1,000 N and r = 0.15 m give a magnitude of 60 Nยทm.