SOLVETUTORMATH SOLVER

Instrument MI-03-077 · Physics

Car Center of Mass Calculator

Put a car on two scales, one under each axle, and the reading tells you exactly where its weight is centered — no jacks, no math by hand, just a moment balance.

Instrument MI-03-077
Sheet 1 OF 1
Rev A
Verified
Type 03 — Vehicle Dynamics SER. 2026-03077

Center of gravity distance from front axle

1.080000 m

CG = (rear weight ⁄ total weight) × wheelbase

The working Every figure verified twice
  1. cgFromFront = 600 ⁄ (900 + 600)·2.7 = 1.080000
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

A car's center of gravity sits somewhere along the wheelbase, closer to whichever axle carries more load. This calculator treats the car as a see-saw pivoting on the front axle: the rear axle's weight, acting at the far end of the wheelbase, must produce the same turning moment as the whole car's weight acting at its CG. Solving that balance gives CG = (rear weight ⁄ total weight) × wheelbase — the rear axle's share of the total load, scaled by how far apart the axles sit.

The result only ever needs two scale readings and one tape measurement, which is exactly how race teams and vehicle certification labs actually find it: drive the car onto corner scales, one pad under each wheel, sum left and right at each axle, and apply the formula. No disassembly, no CAD model, no guessing at where the engine block or fuel tank tips the balance — the scales already include every one of those effects, because they are simply weighing the finished car.

This gives the CG's position along the wheelbase, not its height above the ground. Height needs a second measurement, typically raising one axle a known amount and reading how weight shifts, then applying trigonometry to the tilted car. The fore-aft position computed here still matters on its own: it sets static front-to-rear weight distribution, which governs how braking and cornering grip are split between the axles before any suspension geometry gets involved.

CG=(WrearWfront+Wrear)×L\mathrm{CG} = \left(\dfrac{W_{\text{rear}}}{W_{\text{front}} + W_{\text{rear}}}\right)\times L
CG — center of gravity distance from the front axle, meters (m) · rear weight — load measured at the rear axle, kilograms (kg) · total weight — front weight plus rear weight, kilograms (kg) · wheelbase — front-to-rear axle distance, meters (m). CG grows toward whichever axle is heavier.
  • Enter Front axle weight — the reading from a scale (or scale pair) under the front wheels, in kilograms or pounds.
  • Enter Rear axle weight the same way, from under the rear wheels.
  • Enter Wheelbase, the straight-line distance between front and rear axle centers, in meters or inches.
  • Read Center of gravity distance from front axle — how far back along the wheelbase the CG sits.
  • Divide that result by wheelbase to get the rear weight fraction as a percentage, if you want a distribution figure instead of a distance.

Worked example — a car with 900 kg front, 600 kg rear

A sedan sits on corner scales showing 900 kg total across the front wheels and 600 kg total across the rear, on a 2.7 m wheelbase. Total weight is 1500 kg, so the rear axle carries 600 ⁄ 1500 = 0.4, or 40 percent, of that load. Center of gravity distance from front axle: 0.4 × 2.7 = 1.08 m — just over a third of the way back toward the rear, landing nearer the front axle because that end is doing more of the carrying.

That 1.08 m figure is also 1.62 m forward of the rear axle, since the two distances must add to the full 2.7 m wheelbase. A front-engined layout typically lands the CG somewhere in this front-of-center range; a rear-engined car with most of its mass behind the cabin would instead push the figure past the wheelbase's midpoint, toward the rear.

Questions

Why does the formula use rear weight to find a distance measured from the front?

Because moments balance across the whole wheelbase, and the heavier axle pulls the CG toward itself while the lighter axle pushes it away. Rear weight, divided by total weight, is exactly the fraction of the wheelbase the CG has traveled away from the front pivot. A rear-heavy car (more rear weight) yields a larger fraction and a CG further from the front — which is the correct direction.

Where do I actually get front and rear axle weights?

From a scale. Portable corner scales under all four wheels are standard in racing and give the most accuracy, but a single scale pad under each axle in turn — car held level, parking brake off, tires at rated pressure — works for this calculator, since only the axle totals matter, not the left-right split.

Does this tell me how high the center of gravity sits?

No — only its position along the wheelbase, front to rear. CG height needs a separate procedure: raise one axle a measured amount on a ramp or hoist, record how the weight on the raised axle changes, and apply trigonometry to the tilt angle. Fore-aft position and height are independent measurements answering different questions about handling and rollover risk.

Why is this useful — most owners never move their CG anyway?

Static weight distribution set by this figure decides how braking force and cornering grip should be split between axles, which is why brake bias adjusters and anti-roll bar rates get tuned around it. It also matters loading trailers and light aircraft: shifting cargo changes each axle's or gear's share of the load, and this same balance equation tells you by how much and in which direction.

What happens if one axle carries all the weight?

The CG lands exactly at that axle. Setting front weight to zero puts the entire load, and by extension the entire moment, on the rear axle, and the formula returns the full wheelbase distance — CG sitting right on top of the rear wheels. That is the correct limiting case: a see-saw with nothing on one side balances at the other end, not somewhere in between.

Does tire pressure or suspension setup change this result?

Not directly — the formula only cares about the two axle weight totals and the wheelbase, both of which already reflect whatever the car's actual state is when it sits on the scale. Soft tires or sagging springs would only matter if they changed how much weight each axle bears, which for a car simply resting under gravity they generally do not.

References