Car Center of Mass Calculator

Related Calculators

Wheelbase L: The distance from the front axle center to the rear axle center. It is the main front-to-back length used in the calculator.

Track width T: The distance from the left wheel center to the right wheel center. It is the side-to-side width used for the lateral result.

Front axle weight Fa / Rear axle weight Fb: The total scale reading under the full front axle and full rear axle. These axle loads are used with static equilibrium to locate the center of mass front-to-back.[1]

Left side weight FL / Right side weight FR: The total weight carried by the left wheels and right wheels. They are used to find the side-to-side center of mass.

Center of mass: The balance point of the whole vehicle, often called center of gravity in vehicle work.[1]

Height raised H: How much higher one axle is lifted during the height test. This creates a tilt angle used to estimate vertical center of gravity height from axle load changes.[2]

Wheel radius r: Half the tire diameter. In this method it is added so the final height is reported above the ground rather than from the wheel center line.[2]

Tilt angle theta: The angle made when one end of the car is raised. A bigger angle usually makes the height test easier to measure, as long as the setup stays safe.

Mistake: Mixing inches for "Wheelbase L (selected unit)" with centimeters for "Height raised H (selected unit)" after leaving "Length unit (selected unit)" unchanged.
Fix: Set "Length unit (selected unit)" first and re-enter every distance in that same unit.

Mistake: Entering only one wheel's reading in "Front axle weight Fa (selected weight unit)" or "Rear axle weight Fb (selected weight unit)" instead of the whole axle total.
Fix: Use both front wheels together for "Front axle weight Fa (selected weight unit)" and both rear wheels together for "Rear axle weight Fb (selected weight unit)".

Mistake: Using left-front and right-front wheel readings for "Left side weight FL (selected weight unit)" and "Right side weight FR (selected weight unit)".
Fix: For lateral mode, enter left side total as front-left plus rear-left in "Left side weight FL (selected weight unit)" and right side total as front-right plus rear-right in "Right side weight FR (selected weight unit)".

Mistake: Typing a blank or zero into "Height raised H (selected unit)" for the height test.
Fix: Enter a real raised amount greater than 0 and smaller than "Wheelbase L (selected unit)".

Mistake: Choosing the wrong option in "Which end did you raise for the height test?" so the calculator interprets the weight change backward.
Fix: Match "Which end did you raise for the height test?" to your actual setup, then re-check the raised readings.

Mistake: Ignoring the "Warnings and quick fixes" output when "Total vehicle weight (selected weight unit)" from one setup does not agree with another.
Fix: Re-check scale zeroing, confirm the car was level for the base readings, and compare your sums before trusting the result.

• This calculator assumes the vehicle is still and supported by accurate scales on a firm, level surface for the base measurements.
• Front-to-back results depend on correct "Wheelbase L (selected unit)", "Front axle weight Fa (selected weight unit)", and "Rear axle weight Fb (selected weight unit)" values in the same units.
• Left-to-right results assume "Track width T (selected unit)" matches the side-weight setup you used. If front and rear track differ a lot, using just one track value is an approximation.
• Height results assume the raised-height method was done carefully, with the correct end selected in "Which end did you raise for the height test?" and the raised axle readings entered correctly.
• If "Height raised H (selected unit)" is very small, tiny scale errors can cause a big error in "Center of mass height above ground h (selected unit)".
• Impossible outputs, such as a negative height or a distance outside the wheelbase or track width, usually mean a measurement problem, mixed units, or wrong axle/side totals.
• The optional "Optional: total vehicle weight check (selected weight unit)" is only a consistency check. It does not replace the measured totals in the formulas.

Core idea

The calculator uses balance rules for a vehicle at rest. In plain language, a heavier reading on one end means the center of mass sits closer to the opposite support distance needed to balance that load.[1]

Front-to-back calculation

Fg = Fa + Fb

a = L * (Fb / Fg)

b = L - a

Here, Fg is total vehicle weight, a is distance from the front axle toward the rear, and b is the same location measured from the rear axle toward the front. The calculator also reports front and rear weight percentages from the same axle totals.

front percent = 100 * Fa / (Fa + Fb)

rear percent = 100 * Fb / (Fa + Fb)

Mini-example: If L = 110 in, Fa = 1900 lb, and Fb = 1700 lb, then Fg = 3600 lb. That gives a = 110 * (1700 / 3600) = 51.94 in and b = 110 - 51.94 = 58.06 in.

Left-to-right calculation

Fg_lr = FL + FR

x = T * (FR / Fg_lr)

y = T - x

x is the distance from the left side toward the right, and y is the same center of mass measured from the right side toward the left. If left and right readings are equal, the result lands near the middle of the track width.

Mini-example: If T = 62 in, FL = 1800 lb, and FR = 1800 lb, then Fg_lr = 3600 lb and x = 62 * (1800 / 3600) = 31 in, so y is also 31 in.

Height above ground calculation

The height method compares level axle readings with axle readings after one end is raised. Raising one end creates a tilt angle, and the change in axle load is used to estimate the vertical center of gravity height used in vehicle calculations.[2]

theta = asin(H / L)

cot(theta) = cos(theta) / sin(theta)

front raised: h = ((Fb_p - Fb) / Fg) * L * cot(theta) + r

rear raised: h = ((Fa_p - Fa) / Fg) * L * cot(theta) + r

For front raised, use the change in rear axle weight. For rear raised, use the change in front axle weight. The + r term converts the result to height above ground when r is the wheel radius.[2]

Mini-example: If L = 110 in, H = 8 in, r = 14 in, Fa = 1900 lb, Fb = 1700 lb, and front raised gives Fb_p = 1550 lb, then Fg = 3600 lb and theta = asin(8 / 110) = about 4.17 degrees. Using the formula gives h about 35.65 in.

Checks the calculator applies

The calculator blocks empty required fields for the chosen mode, rejects non-numeric or non-positive required weights, and stops if total weight would be zero. In height mode, it also requires 0 < H < L and rejects setups where the tilt angle is too small to give a reliable result.

It also shows non-blocking warnings when a distance falls outside the wheelbase or track width, when computed height is negative or unrealistically large, or when the optional total-weight check does not agree with the measured totals.

Assumptions behind the math

The method assumes the vehicle is in static equilibrium, the scales are accurate, and the measurements represent complete axle or side totals rather than single-wheel readings.[1] The height method also assumes the raised-height setup was done carefully enough that the axle-load change reflects the tilt test rather than slipping, uneven support, or mixed units.[2]