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.
- 01gamma = 1 / sqrt(1 - 0.81) = 2.294
- 02m_rel = 1 * 2.294 = 2.294 kg
- 03Mass appears 129.4% larger.
Frequently Asked Questions
Is relativistic mass a real concept?
Most modern physicists consider rest mass the fundamental quantity. Relativistic mass is an older concept that equals total energy over c squared. The momentum formula p = gamma * m0 * v is preferred.
Why can nothing reach the speed of light?
As v approaches c, gamma approaches infinity, and the energy required to accelerate further grows without bound. Only massless particles (photons) travel at c.
How fast must you go for the mass to double?
Gamma = 2 when v = c * sqrt(3)/2, which is about 0.866c or 259 600 km/s.
Ready to run the numbers?
Open Relativistic Mass Calculator