Relativistic Mass Calculator Formula
Understand the math behind the relativistic mass calculator. Each variable explained with a worked example.
Formulas Used
Relativistic Mass
rel_mass = rest_mass / sqrt(1 - pow(velocity, 2) / pow(2.998e8, 2))Mass Increase (%)
mass_increase_pct = (1 / sqrt(1 - pow(velocity, 2) / pow(2.998e8, 2)) - 1) * 100Variables
| Variable | Description | Default |
|---|---|---|
rest_mass | Rest Mass (m0)(kg) | 1 |
velocity | Velocity(m/s) | 269800000 |
How It Works
Relativistic Mass
As an object approaches the speed of light, its inertia increases, making further acceleration progressively harder.
Formula
m_rel = m0 * gamma = m0 / sqrt(1 - v^2/c^2)
Note: Modern physics prefers the concept of invariant (rest) mass. The "relativistic mass" is the total energy divided by c^2, but it is a useful pedagogical tool.
Worked Example
1 kg object at 0.9c.
rest_mass = 1velocity = 269800000
- 01gamma = 1 / sqrt(1 - 0.81) = 2.294
- 02m_rel = 1 * 2.294 = 2.294 kg
- 03Mass appears 129.4% larger.
Ready to run the numbers?
Open Relativistic Mass Calculator