Find the mass-weighted position of two bodies on one straight axis. Enter masses in kilograms and positions in metres, measured from the same origin. Positions may be negative, zero or positive.
- Choose an origin and a positive direction along the line.
- Enter each body’s mass in kilograms.
- Enter each body’s signed position in metres from that origin.
- Read the center of mass as a coordinate on the same axis.
For two positive masses, the center of mass lies between their positions and closer to the heavier body. Equal masses place it at the midpoint. If you know only the separation, set body 1 at zero and body 2 at the signed separation.
With the default values, a 2 kg body at 0 m and a 3 kg body at 10 m give (2 × 0 + 3 × 10) ÷ (2 + 3) = 6 m. This is 6 m from body 1 toward body 2.
| Body 1 mass (kg) | Body 1 position (m) | Body 2 mass (kg) | Body 2 position (m) | Center of mass (m) |
|---|---|---|---|---|
| 2 | 0 | 3 | 10 | 6 |
| 4 | -3 | 4 | 5 | 1 |
| 6 | -2 | 2 | 6 | 0 |
| 0 | 8 | 5 | -2 | -2 |
Treat each body as a point mass, or enter the position of each extended body’s own center of mass. Include only the two specified bodies; a connecting rod, support or other component with appreciable mass must also be accounted for separately.
Masses must be nonnegative. One zero mass is allowed and leaves the result at the other body’s position. If both masses are zero, the center of mass is undefined and the calculator returns an unavailable result, not zero. Extremely large values may also produce unavailable results because of numerical limits.
The output is a position relative to your chosen origin, not automatically a distance from either body. Displayed values are rounded to six decimal places.
Image creation required: no registered thumbnail asset was supplied. Create and register a 400 × 400 pixel WebP thumbnail, then insert it as the first image block. Use a cheerful yellow five-point star mascot with hands and no separate legs or feet, a white background, and navy, blue and teal graphics showing two masses and their center of mass on a straight axis. Inspect neighboring tool thumbnails before creation.