Differential Gear Speed Calculator
When a car corners, the outer driven wheel follows a wider arc than the inner one and must turn faster, which is exactly the job an open differential performs. This calculator takes the vehicle speed (the speed of the axle centerline), the turn radius measured to that centerline and the track width, then returns the outer and inner wheel speeds, the speed difference between them and the percentage split. It is pure cornering geometry: each wheel's speed is proportional to the radius of the circle it traces around the turn center.
Differential speed formula
Outer speed = vehicle speed * (radius + track / 2) / radius
Inner speed = vehicle speed * (radius - track / 2) / radius
Speed difference = outer speed - inner speed = vehicle speed * track / radius
Difference (%) = track / radius * 100
Each wheel speed scales with the radius of its arc. The outer wheel traces a circle of radius plus half the track; the inner wheel, radius minus half the track. Their average equals the vehicle (carrier) speed, and the difference equals vehicle speed times track over radius.
Differential context
- An open differential lets the two driven wheels turn at different speeds while averaging the input.
- The outer wheel always turns faster than the inner wheel in a corner.
- A tighter turn (smaller radius) increases the inner-outer speed difference.
- On a gentle highway curve the difference is small; in a tight maneuver it is large.
- Measure the turn radius to the axle centerline and use the track between tire centerlines.
Differential gear speed: frequently asked questions
Why do the two driven wheels turn at different speeds in a corner?
In a turn the outer wheel travels a larger radius than the inner wheel, so it covers more distance in the same time and must rotate faster. An open differential lets the two driven wheels turn at different speeds while their average matches the input from the driveshaft.
How is the wheel speed split calculated?
Each wheel follows a circle: the outer wheel at the centerline radius plus half the track, the inner wheel at the radius minus half the track. Wheel speed is proportional to its radius, so outer and inner speeds scale with those radii while their average is the vehicle speed.
What is the track width?
Track width is the distance between the centerlines of the left and right tires on the same axle. Half the track is how far each driven wheel sits from the vehicle centerline, which sets how much larger the outer wheel's path is than the inner wheel's.
Does an open differential always split speed this way?
An open differential always allows the inner and outer wheels to follow their own arc, with the carrier speed equal to the average of the two wheel speeds. This geometric relation holds as long as both wheels have traction and roll without slipping.
Why does a tight turn increase the speed difference?
The speed difference depends on the ratio of half the track width to the turn radius. A smaller turn radius makes that ratio larger, so the inner and outer wheels differ more in speed. On a gentle highway curve the difference is tiny; in a tight maneuver it is substantial.
Official sources
- NASA Glenn Research Center: Motion in a Circle.
- U.S. Department of Energy: Drivetrain and Differential Basics.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.