Car Center of Mass Calculator — Find the Center of Gravity of Your Car (Metric & Imperial)

Car Center of Mass Calculator

The car center of mass calculator is a handy tool that estimates the location of an essential parameter of your car that you can't determine at first glance – the center of gravity. All you need is a car scale and the computations implemented in our car center of gravity calculator.

In the following article, you will find step-by-step instructions on how to find the center of gravity of a car, the importance of this quantity (especially race car center of gravity), and the physics behind it.

What are the physics behind the calculations?

The center of mass (or the center of gravity) has various definitions. Regarding vehicles, we can say that this is a unique point at which a car behaves as if all its mass were centered at that point. If you apply any force to this specific point, a vehicle will start to move in the direction of that force without rotating. To fully describe the center of mass of a three-dimensional object, you need to estimate three coordinates:

• Longitudinal position — determined by distances a and b;
• Altitudinal position — determined by height h; and
• Side position — determined by distances x and y.

Where these three coordinates intersect in space is the actual center of mass. Determination of the center of gravity consists of a few weight measurements of the car in different geometries. Additionally, you need to measure such parameters as the wheelbase L (distance between the front and rear axles), the radius of the wheels r, the height at which the wheels were raised H (in the case of altitudinal location), and the car track T in the case of side location (distance between the wheels on the same axle).

How to find the center of gravity of a car

1. Longitudinal position (distances a and b)

1. Enter the total weight of your car – for example, 3000 lb.
2. Find the wheelbase of your car – the distance between the centers of two wheels of different axles. Let's say it is 8 ft.
3. Ride up with the front (or rear) wheels on the scale and measure the weight of that axle. Both axles should be on the same level! The measured mass should be roughly half of the total mass – for example, 1800 lb.
4. Read the resulting distances a and b. In our example, a = 3.2 ft and b = 4.8 ft, meaning the center of gravity is slightly shifted to the front – the most frequent situation, since the heavy engine usually sits under the front hood.

b = L · W_f / W    and    a = L − b

2. Altitudinal location (height h)

1. Find the longitudinal position first (you can use this calculator).
2. Decide which axle you will raise – front or rear.
3. Enter the height H at which the chosen axle was raised compared to the other axle. The higher you lift the wheels, the more accurate the result. A height of about 15 inches (1.25 ft) is usually high enough.
4. Enter the radius r of the car wheels (the distance from the axle to the ground).
5. Measure the weight of the grounded axle in both the level and raised configurations. The grounded axle gets a little heavier when the other end is lifted.
6. Read the resulting height h, the height of the center of mass above the ground.

h = r + (L · √(L² − H²) / H) · (ΔW / W)

3. Side location (distances x and y)

1. Enter the total weight of your car – for example, 3000 lb.
2. Find the car track T – the distance between the centers of two wheels on the same axle. Let's say it is 4 ft.
3. Ride up with the left (or right) wheels on the scale and measure their weight, e.g. 1550 lb of the left wheels.
4. Read the resulting distances x and y. In our example, x ≈ 1.93 ft and y ≈ 2.07 ft. Cars are usually symmetric in weight distribution in the front view, so x ≈ y.

Before you begin your measurements: all baggage and people inside a car influence the center of mass. Make sure your tire pressures are correct and your car is tanked with fuel (if required). If you're doing measurements alone, use weights that resemble your weight in the driver's seat.

The importance of the center of gravity

The weight distribution is essential in vehicle handling. It defines the car's response to a driver's inputs and how it moves along the road. A race car's center of gravity is crucial for balance and steering.

The longitudinal position of the center of mass, related to the wheelbase, determines the load transfer between the front and rear wheels. The car tilts forward and backward during braking and acceleration. A vehicle with a much higher weight load on the rear axle tends to understeer – it does not turn enough and leaves the road. A much greater weight load on the front axle leads to oversteer – the vehicle turns more sharply than intended and could even spin.

The altitudinal position of the center of mass, related to the car track, determines the load transfer from side to side – important when cornering. Cars with a high altitudinal center of mass are more likely to tilt on turns and may even topple. A lower race car's center of gravity is a principal performance advantage, especially compared to SUVs. This is why Formula One cars are so low (their center of gravity is only about 10 inches high).