What units should I use?

Any consistent unit set works — SI (m/s, m) is standard. If you enter wheel speeds in m/s and dimensions in meters, all outputs are in m/s, rad/s, and meters. Mixing units (e.g. cm for radius, m/s for speed) will give incorrect results.

What does a negative angular velocity mean?

A negative omega means the robot is turning clockwise (right) when viewed from above. Positive omega is a counter-clockwise (left) turn.

What happens when both wheel speeds are equal?

Equal speeds produce omega = 0 and an infinite turning radius, meaning the robot moves in a straight line. The ICC offset is shown as "infinity" in that case.

What is spin-in-place?

When both wheels spin at the same speed but in opposite directions (v_L = -v_R), linear velocity is zero and the robot rotates around its own center. The turning radius is 0.

Does this model account for wheel slip?

No. The equations assume ideal no-slip rolling contact. For surfaces with significant slip, a slip-compensated or odometry-corrected model is needed.

The Instantaneous Center of Curvature is the point around which the robot is currently rotating. It lies on the axle line, at a distance R to the left of the robot's center (positive R = left turn).

Differential Drive Kinematics Calculator

Name: Differential Drive Kinematics Calculator
Availability: InStock
Author: Nham Vu

Enter left/right wheel speeds, wheel radius, and axle width to compute a differential-drive robot's linear velocity, angular velocity, turning radius, and ICC offset.

Robot Parameters

Left wheel speed (v_L)

m/s

Right wheel speed (v_R)

m/s

Wheel radius (r)

Axle width (L)

Or enter wheel RPM instead

Left RPM

Right RPM

Filling RPM fields overwrites the speed fields above using the wheel radius.

Motion Type

—

Linear Velocity (v)

—

m/s

Angular Velocity (ω)

—

rad/s

Turning Radius (R)

—

m (from robot center)

ICC Offset

—

m along axle (+ = left)

Derived Values

Curvature κ = 1/R: —
Arc angle per second: —
Speed difference (v_R − v_L): —
Average wheel speed: —

Top-View Diagram

Summary