Car Center of Mass Calculator finds the center of gravity of a car from axle or corner scale weights, as distances behind the front axle, from the left wheels and above the ground.
Weigh the car on level ground: the whole car, the front axle alone, then the left wheels alone.
Height Test and Result Unit
Car Diagram
Step-by-Step Working
- Known values: L = 8 ft, T = 4 ft, car weight W = 3,000 lb, front axle = 1,800 lb, left wheels = 1,550 lb
- Rear axle weight: W − front axle = 3,000 − 1,800 = 1,200 lb
- Behind the front axle: a = L × rear axle ÷ W = 8 ft × 1,200 ÷ 3,000 = 3.2 ft
- Ahead of the rear axle: b = L − a = 4.8 ft
- Right wheels weight: W − left wheels = 1,450 lb
- From the left wheels: x = T × right wheels ÷ W = 4 ft × 1,450 ÷ 3,000 = 1.93333 ft, and y = T − x = 2.06667 ft
- Tilt angle: θ = sin⁻¹(H ÷ L) = sin⁻¹(0.15625) = 8.9893°
- Front axle change when raised: 1,800 − 1,750 = 50 lb
- Height: h = change ÷ W × L ÷ tan θ + r = 50 ÷ 3,000 × 8 ft ÷ 0.158193 + 1 ft = 1.84285 ft
- Result: a = 3.2 ft, x = 1.93333 ft, h = 1.84285 ft
Axle Loads Under Braking
| Braking | Front (lb) | Rear (lb) |
|---|---|---|
| 0 g | 1,800 | 1,200 |
| 0.3 g | 2,007 | 992.7 |
| 0.5 g | 2,146 | 854.5 |
| 0.8 g | 2,353 | 647.1 |
| 1 g | 2,491 | 508.9 |
Car Center of Mass Calculator from Scale Readings
The center of mass of a car is the single point where all of its weight can be treated as acting. It is also called the center of gravity, or CG. Its position decides how the weight is shared between the four tires, and how that share changes when the car brakes or turns.
The Car Center of Mass Calculator finds that point in three directions from scale readings. It gives the distance behind the front axle, the distance from the left wheels and the height above the ground. Nothing has to be taken apart, because the scales under the wheels do the measuring.
The Scale Readings menu has two ways to enter the weights. Axle and side totals takes the whole car, the front axle alone and the left wheels alone. Four corner scales takes one reading per wheel and adds them up for you.
The starting entries are a 3,000 lb car with an 8 ft wheelbase and 1,800 lb on the front axle. The main result reads 3.2 ft Behind the Front Axle. Weights can be in pounds or kilograms, and lengths in feet, inches, meters, centimeters or millimeters.
How to Calculate the Center of Mass of a Car
Each direction uses the same idea. The car is balanced on its wheels, so the heavier end or side must sit closer to the center of mass. A simple ratio of two scale readings then gives the distance.
Front to Rear Position
Weigh the whole car and the front axle on level ground. The rear axle weight is the difference. The distance a from the front axle to the center of mass is the wheelbase L times the rear share of the weight.
$$a = L \times \frac{W_{rear}}{W}$$
$$b = L – a$$
For the example, the rear axle carries 3,000 − 1,800 = 1,200 lb. So a = 8 × 1,200 ÷ 3,000 = 3.2 ft, and b = 4.8 ft ahead of the rear axle. The first result card of the Car Center of Mass Calculator also shows the split as 60% / 40% front to rear.
Side to Side Position
The same ratio works across the car, with the track width T in place of the wheelbase. The distance x from the left wheels uses the weight on the right wheels, measured between the tire centers.
$$x = T \times \frac{W_{right}}{W}$$
With a 4 ft track and 1,550 lb on the left wheels, the right wheels carry 1,450 lb. That gives x = 4 × 1,450 ÷ 3,000 = 1.933 ft and y = 2.067 ft from the right wheels. The center of mass sits 0.06667 ft to the left of the centerline.
The third card states this as 51.67% on the Left Wheels, with the left side 100 lb heavier than the right. A driver sitting alone in the car is often enough to cause a gap of that size.
Center of Mass Height
Height cannot be read from level scales. It needs a second weighing with one axle raised. Tilting the car moves some weight onto the lower axle, and the taller the center of mass, the more weight moves.
$$\theta = \sin^{-1}\left(\frac{H}{L}\right)$$
$$h = \frac{\Delta W}{W} \times \frac{L}{\tan\theta} + r$$
H is the height the axle was raised, ΔW is the change in the front axle reading and r is the wheel radius. The first term is the height above the wheel centers. Adding r gives the height above the ground.
In the example the front wheels are raised 15 in, so θ = sin⁻¹(15 ÷ 96) = 8.989°. The front axle reading drops from 1,800 to 1,750 lb, a change of 50 lb. Then h = 50 ÷ 3,000 × 8 ÷ 0.1582 + 1 = 1.843 ft above the ground.
Longacre Racing, which makes racing scales, uses the same equation with the rear end raised. Its procedure calls for full fluids, solid links in place of the shocks, and tires at maximum pressure, so that nothing sags during the test. It suggests raising the car at least 10 inches.
In the Car Center of Mass Calculator, the Height Test option covers front wheels raised, rear wheels raised or not measured. If the height test is skipped, the fourth card reads No Height Test Entered and the other three results still work.
Center of Mass Formula
The car method is a special case of the general centre of mass formula. OpenStax University Physics defines the center of mass as the weighted average position of the mass. To calculate the center of mass of a system, multiply each mass by its position, add the products and divide by the total mass.
$$x_{cm} = \frac{m_{1} x_{1} + m_{2} x_{2} + \dots + m_{n} x_{n}}{m_{1} + m_{2} + \dots + m_{n}}$$
To find the center of mass in two dimensions, apply the formula once for x and once for y. A center of gravity calculator in 3D adds a third line for z. Each direction is worked out separately from the others.
How to Find the Center of Mass for 3 Masses
Take masses of 2 kg at (0, 0), 3 kg at (4, 0) and 5 kg at (4, 3), with coordinates in meters. The total mass is 10 kg. The x coordinate is (2 × 0 + 3 × 4 + 5 × 4) ÷ 10 = 3.2 m. The y coordinate is (5 × 3) ÷ 10 = 1.5 m.
How to Find the Center of Mass with Coordinates
The four wheel scales of a car are four masses with known coordinates. Put the front axle at 0 and the rear axle at 8 ft. With 925 and 875 lb on the front scales and 625 and 575 lb on the rear, the formula gives (1,200 × 8) ÷ 3,000 = 3.2 ft. That matches the axle method exactly.
This is why the tool also works as a 2D center of mass calculator for a car. The Four corner scales setting reads the four numbers and returns both coordinates. The Car Diagram panel marks the point on a top view and a side view.
Center of Mass Formula for Different Shapes
For a solid object the sum becomes an integral over the mass, which is how the center of mass is calculated in Calc 3. For a uniform shape it reduces to the geometric center. A few standard results are worth knowing.
| Uniform shape | Where the center of mass is located |
|---|---|
| Rod, rectangle, box, sphere | At the geometric center |
| Triangle | One third of the height above the base |
| Semicircle of radius R | 4R ÷ (3π) from the straight edge |
| Solid hemisphere of radius R | 3R ÷ 8 from the flat face |
| Solid cone of height h | h ÷ 4 above the base |
The center of mass does not have to be inside the material. OpenStax notes that a doughnut has its center of mass in the hole. For the Earth and Moon together, it lies about 4,640 km from Earth’s center, which is still inside the Earth.
How to Find the Center of Mass of an Irregular Object
Hang the object from one point and draw a vertical line down from that point. Hang it from a second point and draw another line. The center of mass is where the lines cross. A car is an irregular object too heavy to hang, which is why scales are used in place of a plumb line.
A person’s own center of mass can be located with the car method. Lie on a board supported by a scale at each end. The two readings and the board length give the position along the body, using the same ratio as the wheelbase formula.
What the Center of Mass Height Tells You
Height matters most for rollover. NHTSA defines the static stability factor as half the track width divided by the center of gravity height. A higher value means the car resists tipping better, and NHTSA’s rollover star ratings are built on it.
$$SSF = \frac{T}{2h}$$
The fourth result card of the Car Center of Mass Calculator shows this as Stability factor (T ÷ 2h). The example car scores 1.085, because its 4 ft track is narrow for its height. A NHTSA technical report put model year 2003 passenger cars at an average of 1.41 and SUVs at 1.17.
Height also sets how much load moves forward under braking. The shift is the car weight times the braking rate in g times h ÷ L. The Axle Loads Under Braking panel lists the result for the example car.
| Braking | Front axle (lb) | Rear axle (lb) |
|---|---|---|
| 0 g | 1,800 | 1,200 |
| 0.3 g | 2,007 | 992.7 |
| 0.5 g | 2,146 | 854.5 |
| 0.8 g | 2,353 | 647.1 |
| 1 g | 2,491 | 508.9 |
At 1 g the front axle carries 83% of the weight, up from 60% at rest. That is why front brakes are larger than rear ones. The Stopping Distance Calculator gives the braking rate for a dry or wet road.
Each axle load is a normal force from the road, and tire grip depends on it. The Normal Force Calculator covers that link. In a corner the same height moves load to the outside wheels, and the Angle of Banking Calculator shows how a banked road reduces the side force.
Corner Weights and Cross Weight
With the Four corner scales setting, the third card of the Car Center of Mass Calculator changes to cross weight. Cross weight is the front right plus rear left readings as a percentage of the total. Racers also call it wedge.
The starting corner readings are 925, 875, 625 and 575 lb. The front right and rear left add to 1,500 lb, so the cross weight is exactly 50%. At 50% the car behaves the same in left and right turns.
Cross weight can be changed without moving the center of mass. Raising one spring perch shifts load diagonally between the scales. The axle totals and the side totals stay the same, so the Car Center of Mass Calculator returns the same a and x.
How Much Does a Car Weigh?
The mass of a normal car depends on its type. The EPA Automotive Trends Report puts the average new US vehicle at 4,354 lb for model year 2024. That is about 1,975 kg, or close to 2 metric tons.
| Vehicle type (model year 2024) | Average weight (lb) | In kg |
|---|---|---|
| Sedan or wagon | about 3,700 | about 1,680 |
| Car SUV | about 4,200 | about 1,905 |
| Minivan or van | about 4,500 | about 2,040 |
| Truck SUV | about 4,600 | about 2,085 |
| Pickup | about 5,100 | about 2,315 |
So 2 tons is not heavy for a car today. It is the weight of a typical new SUV. A car of 1,200 kg or 1,400 kg is light by this measure, since both are below the average sedan. A car at 1,000 kg, which is 1 metric ton, is in small city car and lightweight sports car territory.
Cars near 500 kg are microcars and quadricycles. Citroën, for example, classes its 2.41 m long Ami as a light quadricycle. A 200 kg vehicle is lighter than any road car, closer to a large motorcycle.
| Mass (kg) | Pounds (lb) | US short tons | Weight as a force (N) |
|---|---|---|---|
| 200 | 440.9 | 0.22 | 1,961 |
| 500 | 1,102 | 0.55 | 4,903 |
| 1,000 | 2,205 | 1.10 | 9,807 |
| 1,200 | 2,646 | 1.32 | 11,768 |
| 1,400 | 3,086 | 1.54 | 13,729 |
| 2,000 | 4,409 | 2.20 | 19,613 |
A 200 kg car therefore weighs 1,961 N, and 1,200 kg in weight is 11,768 N or 2,646 lb. To calculate the weight of a car as a force, multiply its mass by 9.80665, which the kg to Newtons Calculator does for any mass.
To find how heavy your own car is, check the curb weight in the owner’s manual or on the registration papers. To measure the real figure with fuel and cargo, drive onto a public weighbridge or truck scale. Weighing each axle there gives the first two entries the Car Center of Mass Calculator needs.
Excel Sheets and Vehicle CG Databases
A car center of mass calculator in Excel needs only the formulas above. Put the four corner weights in cells, and write the wheelbase times the rear total divided by the grand total. For a list of parts, SUMPRODUCT of the masses and positions divided by SUM of the masses gives the center of gravity.
For a vehicle center of gravity database, the main public source is NHTSA’s own test data. An SAE paper from 2021 lists center of gravity measurements for 1,472 vehicles in total, including 448 tested from 2009 through August 2020.
Published figures are for an empty car. Passengers, fuel and cargo all move the point, so scale readings of your own car as driven are the better input. More force and motion tools are listed under Dynamics and Statics Calculators.