Select kinetic energy, mass, or momentum magnitude as the unknown, then enter the two known values. This calculator uses the non-relativistic model for a positive-mass body moving much slower than light.
Momentum from Energy Formula
The following equation is used to calculate the Momentum from Energy.
- Where p is the Momentum from Energy (m/s*kg)
- KE is the total kinetic energy (joules)
- m is the mass (kg)
For a non-relativistic body with positive mass, momentum magnitude is √(2mKE). Kinetic energy and mass determine the magnitude, not the direction. The result is not the photon relation or a relativistic total-energy conversion.
| Energy (J) | Momentum (kg·m/s) | Momentum (g·cm/s) | Momentum (lb·ft/s) |
|---|---|---|---|
| 0.5 | 1.000 | 100000 | 7.233 |
| 1 | 1.414 | 141421 | 10.229 |
| 2 | 2.000 | 200000 | 14.466 |
| 5 | 3.162 | 316228 | 22.873 |
| 10 | 4.472 | 447214 | 32.347 |
| 20 | 6.325 | 632456 | 45.746 |
| 50 | 10.000 | 1000000 | 72.330 |
| 100 | 14.142 | 1414214 | 102.290 |
| 200 | 20.000 | 2000000 | 144.660 |
| 500 | 31.623 | 3162278 | 228.728 |
| 1000 | 44.721 | 4472136 | 323.470 |
| 2000 | 63.246 | 6324555 | 457.456 |
| 5000 | 100.000 | 10000000 | 723.301 |
| 10000 | 141.421 | 14142136 | 1022.903 |
| 20000 | 200.000 | 20000000 | 1446.603 |
| 50000 | 316.228 | 31622777 | 2287.280 |
| 100000 | 447.214 | 44721360 | 3234.702 |
| 200000 | 632.456 | 63245553 | 4574.560 |
| 500000 | 1000.000 | 100000000 | 7233.014 |
| 1000000 | 1414.214 | 141421356 | 10229.026 |
| Non-relativistic relation: p = √(2 m E). Values assume m = 1.00 kg. Momentum unit factors: 1 kg·m/s = 100000 g·cm/s ≈ 7.233014 lb·ft/s. | |||
What are the units for Momentum from Energy?
The most common units for Momentum from Energy are m/s*kg.
How to Calculate Momentum from Energy?
Example Problem:
The following example problem outlines the steps and information needed to calculate the Momentum from Energy.
First, determine the total kinetic energy. In this example, the total kinetic energy is determined to be 500 (joules).
Next, determine the mass. For this problem, the mass is measured to be 12 (kg).
Finally, calculate the Momentum from Energy using the formula above:
p = SQRT( 2*KE / m) * m
Inserting the values from above and solving the equation with the input values gives:
p = SQRT( 2*500/ 12) * 12 = 109.54 (m/s*kg)
