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

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

A differential-drive robot steers by varying the speeds of its two independently driven wheels. This calculator applies the standard unicycle kinematic model to compute linear velocity (v), angular velocity (omega), turning radius (R), and the location of the instantaneous center of curvature (ICC) relative to the robot's center. Results update in real time as you adjust any input.

How it works

Enter the left and right wheel surface speeds (m/s or any consistent unit).
Provide the wheel radius (r) and the axle width — the center-to-center distance between the two wheels (L).
The calculator derives linear velocity v = (v_R + v_L) / 2.
Angular velocity omega = (v_R - v_L) / L is computed next.
Turning radius R = v / omega (infinite when driving straight) and ICC offset from center = R are displayed.
The motion type (straight, spin-in-place, or curved turn) is identified automatically.

Use cases

Verify robot motion parameters before programming a microcontroller.
Tune PID controllers by checking the expected angular rate for a given speed differential.
Calculate ICC position for path-planning algorithms.
Prototype wheel speed setpoints for arc maneuvers in ROS or similar frameworks.
Teach mobile-robot kinematics concepts in a classroom or lab setting.
Debug chassis geometry by comparing predicted vs. measured turning radii.
Quickly convert RPM inputs to ICC and curvature for custom drive bases.
Validate simulation parameters against real-world axle and wheel dimensions.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu