How to Find a Car's Center of Mass (Longitudinal Position)
A car's longitudinal center of gravity (CG) — the fore-aft point where its entire weight can be treated as concentrated — can be located without any special lab equipment, just a set of axle or corner scales and a tape measure. Parked on level ground, a car behaves like a rigid beam resting on two supports: the front axle and the rear axle. How much weight each axle carries depends entirely on how far the CG sits from that axle, so measuring the two axle weights and the wheelbase is enough to solve for the CG position.
The moment-balance formula
- Let Wf be the front axle weight, Wr the rear axle weight, W = Wf + Wr the total weight, and L the wheelbase (the distance between the front and rear axle centerlines).
- Taking moments about the front axle and setting the sum to zero for static equilibrium gives Wr × L = W × df, so the distance from the front axle to the CG is df = (Wr / W) × L.
- By the same logic about the rear axle, the distance from the rear axle to the CG is dr = (Wf / W) × L = L - df.
- This is the same statics as a see-saw: the axle closer to the CG always reads the heavier weight, because a support nearer a load on a two-point beam carries the larger share of it.
Measuring axle weights accurately
- Weigh the car on a level, flat surface, and decide up front whether you want the curb-weight CG (empty car, full fluids) or the loaded CG (with driver, passengers, or cargo included) — be consistent about which one you enter.
- Use axle scales, or sum the left and right corner-scale readings for each axle, rather than a single bathroom scale under one wheel.
- Measure the wheelbase as the horizontal distance between the front and rear axle centerlines, not the car's overall bumper-to-bumper length — a small wheelbase error shifts the calculated CG position directly.
- Remember this method finds the longitudinal (fore-aft) CG only; the vertical CG height requires a separate tilt-table or incline weighing test.
Frequently Asked Questions
What is the formula for a car's center of gravity position?
The distance from the front axle to the center of gravity is df = (Wr / W) × L, where Wr is the rear axle weight, W is the total vehicle weight, and L is the wheelbase. The distance from the rear axle is dr = (Wf / W) × L = L - df. Both come from balancing moments about each axle when the car is treated as a beam supported at two points.
Why does the axle carrying more weight end up closer to the center of gravity?
For a beam resting on two supports, the support nearer the load always carries the larger share of the weight. So if the front axle reads heavier than the rear, the center of gravity sits closer to the front axle, and vice versa — the same statics as a see-saw.
Does this calculator give the height of the center of gravity?
No. This method finds only the longitudinal (fore-aft) position of the center of gravity from level-ground axle weights. Finding the center of gravity's height requires a separate tilt-table or ramp test that compares axle weights at a known incline angle.