Relativity
Every relativity calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
8 calculators in this section
- Gravitational Time Dilation CalculatorA clock higher up runs faster. This page works the Schwarzschild factor for two clocks at two radii and gives you the microseconds per day between them — then adds the speed correction for an orbiting clock, which is how the famous 38 microseconds a day of the GPS correction is actually built.
- Ladder and Barn Paradox CalculatorA ladder too long for a barn fits inside it when it runs fast enough — and does not, in its own frame, at the same time. Both frames are right. This page takes your ladder, your barn and your speed and tells you what each frame sees, and why the disagreement is about simultaneity rather than about length.
- Length Contraction Calculator (L = L₀/γ)A rest length and a speed in; the contracted length, the metres lost and the direction rule out. The one that costs marks is the direction: only the dimension along the motion shrinks, so a metre cube becomes a slab, not a smaller cube.
- Lorentz Factor Calculator (γ from β)γ from a speed, the speed back from a γ you need, and the curve drawn with your own β marked on it — because the only thing that matters about γ is where it stops being 1, and that happens later and then faster than anybody expects.
- Relativistic Kinetic Energy CalculatorKE = (γ − 1)mc² and p = γmv, with the headline answering the question that actually matters: by what factor has ½mv² stopped being good enough? Both curves are drawn on one axis so you can see where they part company.
- Relativistic Space Travel CalculatorHow long a star journey takes, in two answers that are both right: the years that pass on Earth and the years the crew actually live through. Constant velocity is the headline; the constant-1g rocket, which is the one that makes the galaxy reachable, is worked out beside it.
- Relativistic Velocity Addition CalculatorThrow a ball forwards from a fast rocket and the speeds do not simply add. This page does the real sum, shows the wrong one beside it, and draws the gap between them — because the gap is the whole point, and it is the clearest thing in relativity to show a child.
- Time Dilation Calculator (Δt = γΔt₀)Give it a proper time and a speed and it returns the dilated interval, the Lorentz factor, and the gap between the two clocks — with the muon that reaches the ground and the GPS satellite that loses 7 microseconds a day worked out from the same two lines of algebra.