What formula does this calculator use?

It uses T = I × α, where α (angular deceleration) = ω₀ / t. I is the moment of inertia in kg·m², ω₀ is the initial angular velocity in rad/s, and t is stopping time in seconds.

How do I convert RPM to rad/s?

Multiply RPM by 2π/60 ≈ 0.10472. For example, 1500 RPM = 1500 × 0.10472 ≈ 157.08 rad/s. The calculator handles this conversion when you select RPM as the input unit.

What is moment of inertia and where do I find it?

Moment of inertia (I) measures how mass is distributed around the rotation axis. For a solid disc: I = ½mr². For a hollow cylinder: I = ½m(r_outer² + r_inner²). Manufacturer datasheets for flywheels and motor rotors usually list I directly.

What does the tangential force result mean?

If you provide a rotor radius, the tool divides torque by radius (F = T / r) to give the equivalent linear force at the rotor rim. This is useful for sizing brake pad clamping force or checking caliper capacity.

Does this account for friction or heat?

No. This is a pure inertial torque calculation. Real systems require additional torque to overcome friction losses and must account for heat dissipation in the brake material. Add a safety factor (typically 1.5–2×) for practical designs.

Brake Torque Calculator

Enter moment of inertia, initial angular velocity, and stopping time to calculate required braking torque using T = I × (ω / t).

Inputs

T = I × α | α = ω / t

Moment of Inertia (I)

kg·m²

Initial Angular Velocity (ω₀)

Stopping Time (t)

Rotor Radius (optional)

Enables tangential braking force output (F = T / r).

Results

Fill in the inputs and click Calculate.

Formula Reference

T = I × α Braking torque (N·m)

α = ω / t Angular deceleration (rad/s²)

F = T / r Tangential force at rim (N)

ω = RPM × 2π/60 RPM to rad/s

Summary

This tool calculates the braking torque required to bring a rotating object to a complete stop. It applies Newton's second law for rotation: T = I × α, where angular deceleration α = ω / t. Enter the moment of inertia, initial angular velocity, and desired stopping time to find the torque the brake must supply.

How it works

Enter the moment of inertia (I) of the rotating mass in kg·m².
Enter the initial angular velocity (ω) in rad/s or RPM — the tool converts automatically.
Enter the stopping time (t) in seconds.
The tool computes angular deceleration α = ω / t.
Braking torque is returned as T = I × α in Newton-meters (N·m).
Optional: enter rotor radius to see the equivalent tangential braking force.

Use cases

Sizing brake pads or disc brakes for industrial rotating machinery.
Selecting motor brakes for servo and spindle drive systems.
Checking that an emergency stop brake can halt a flywheel within a safe time.
Calculating holding torque for conveyor belt drive pulleys.
Verifying brake torque margins in wind turbine yaw and pitch systems.
Academic rotational dynamics problems involving angular deceleration.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu