Wheel Force Calculator - Calculator Academy

Reviewed By: Patrick Myers (BSME)

Enter the vehicle’s mass, acceleration, and number of driven wheels into the calculator to determine the average wheel (tractive) force per driven wheel.

Wheel Force Formula

The following simplified equation is used to calculate the average wheel (tractive) force per driven wheel (neglecting rolling resistance, aerodynamic drag, grade, and drivetrain losses).

WF = VM * A / W_d

Where WF is the average wheel (tractive) force per driven wheel (N)
VM is the vehicle mass (kg)
A is the vehicle acceleration (m/s²)
W_d is the number of driven wheels

To calculate the wheel force (per driven wheel), multiply the vehicle mass by the acceleration, then divide by the number of driven wheels.

What is a Wheel Force?

Definition:

Wheel (tractive) force is the longitudinal force at the tire–road contact patch that the driven wheels apply to the ground (and the ground applies back on the tires). In this calculator, “wheel force” means the average tractive force per driven wheel required to produce a given acceleration on level ground while ignoring resistive forces.

How to Calculate Wheel Force?

Example Problem:

The following example outlines the steps and information needed to calculate the Wheel Force.

First, determine the vehicle mass. In this example, the vehicle mass is found to be 1000kg.

Next, determine the vehicle acceleration. For this problem, the vehicle acceleration is found to be 15 m/s².

Next, determine the number of driven wheels. In this case, the car has 4 driven wheels.

Finally, calculate the Wheel Force using the formula above:

WF = VM * A / W_d

WF = 1000 * 15 / 4

WF = 3,750 N

FAQ

What factors can affect the wheel force of a vehicle?

The actual wheel (tractive) force available or required can be affected by the vehicle’s mass, desired acceleration, the number of driven wheels, tire–road friction (traction), road surface/conditions, terrain/grade, aerodynamic drag, rolling resistance, and drivetrain losses. This calculator uses a simplified relationship based on F = m·a and does not include drag, rolling resistance, grade, or drivetrain efficiency.

How does tire pressure influence wheel force?

Tire pressure can influence the available traction and how effectively forces are transmitted at the contact patch (via changes in the tire’s characteristics and contact behavior). While tire pressure does not appear explicitly in the simplified equation on this page, it can affect real-world acceleration and the maximum wheel force before wheel slip occurs.

Why is it important to calculate wheel force in vehicle design?

Estimating wheel (tractive) force helps engineers size and evaluate powertrains, tires, and driveline components and predict acceleration performance. More detailed design work typically includes resistive forces (drag, rolling resistance, grade), weight transfer, tire models, and drivetrain efficiency in addition to the simplified F = m·a relationship.

Follow-Up Calculations

If your wheel force comes out to 450 lb at 60 mph, that works out to about 72 wheel horsepower because power is force multiplied by speed. You can estimate horsepower at the wheels from the same force-and-speed relationship, which makes it easier to compare dyno numbers with what actually reaches the pavement.

A result of 72 whp often corresponds to roughly 85 hp at the crank if you assume about 15% drivetrain loss, so around 13 hp disappears through the transmission and differential. If you want to work back to crank output, this is the quickest way to judge how much engine power is being lost before it reaches the tires.

If your wheel force is 600 lb and your car weighs 3,600 lb, the vehicle can accelerate at about 0.17 g before aerodynamic drag and other losses are added in. You can estimate acceleration from horsepower to see how a given power level translates into real-world launch and passing performance.