Hong Life CalculatorsUnderstanding the car centre of gravity calculator — concept and principle
A car's centre of gravity (CG) affects handling, braking, rollover risk and weight transfer. This calculator finds where the CG sits along the wheelbase and across the track from axle and wheel loads, and estimates its height using the axle-raising method.
How it is calculated
- Longitudinal: a = Wr × L ÷ W, the distance of the CG behind the front axle (W = Wf + Wr).
- Lateral: distance from the right wheels = Wleft × track ÷ W, shown as an offset from the centreline (+ = towards the left).
- Height: raise the front axle by H so the car tilts by θ = arcsin(H ÷ L), weigh the rear axle again, then h = r + L × ΔWr ÷ (W × tan θ), with r the loaded wheel radius.
The principle
The CG is the balance point of the weights. Taking moments about the front axle, the rear axle carries a share of the weight proportional to how far back the CG sits. To find its height, the car is tilted: because the CG is above the axle line, tilting shifts a little extra weight onto the lower axle. The size of that shift reveals how high the CG is. Suspension movement and fuel slosh can swamp the small change, so the suspension should be locked and the lift should be large.
Worked example
Default inputs: wheelbase 2,700 mm; front 850 kg, rear 650 kg; track 1,580 mm, left wheels 760 kg; front raised 400 mm, rear load then 669 kg; wheel radius 320 mm.
- Total mass = 1,500 kg; front share 56.7%, rear 43.3%.
- CG behind the front axle = 650 × 2,700 ÷ 1,500 = 1,170 mm; ahead of the rear axle = 1,530 mm.
- Lateral: 760 × 1,580 ÷ 1,500 ≈ 800.5 mm from the right wheels, 11 mm left of centre.
- Tilt θ = arcsin(400 ÷ 2,700) ≈ 8.52°; ΔWr = 669 − 650 = 19 kg.
- h = 320 + 2,700 × 19 ÷ (1,500 × tan 8.52°) ≈ 548 mm.
| Wheelbase L (mm) | CG behind the front axle (mm) |
|---|---|
| 675 | 293 |
| 1,350 | 585 |
| 2,025 | 878 |
| 2,700 | 1,170 |
| 3,375 | 1,463 |
| 4,050 | 1,755 |
| 5,400 | 2,340 |
How to read the result
A lower CG reduces weight transfer and body roll; a CG well forward gives more front-axle load. Typical passenger-car CG heights are roughly in the 500–600 mm range, though values vary by vehicle type. Small weighing errors strongly affect the height, so repeat measurements.
Common mistakes
- Not locking the suspension or not fixing the fuel level before the tilt test.
- Using too small a lift, making ΔWr tiny and uncertain.
- Using an unloaded wheel radius.
- Mixing kilograms and newtons between readings.
Frequently asked questions
How do you find a car's centre of gravity height?
Weigh the axles level, raise one axle a known height, weigh again and use the change in load.
Why does weight distribution matter?
It affects grip balance, braking and handling, especially when cornering.
Why lock the suspension?
Suspension movement during the tilt shifts weight and distorts the small load change.
Sources: Gillespie, T. D., Fundamentals of Vehicle Dynamics. SAE International (1992) · Milliken, W. F. & Milliken, D. L., Race Car Vehicle Dynamics. SAE International