Four interactive graphs exploring time dilation, length contraction, the rocket equation, and relativistic kinetic energy.
Right-click and hold anywhere on a graph to see exact values.
Double-click on a graph to zoom the x-axis around that point.
Double-click outside any graph to reset all zoom.
How much time passes on a moving clock for every 1 second of Earth time. Both axes are logarithmic — the interesting behavior is near v = c. Formula: t' / t = √(1 − v²/c²) = 1/γ
How long a 1 light-year ruler appears to an observer moving past it. Same formula as time dilation — moving rulers shrink by the same factor moving clocks slow. Formula: L' / L = √(1 − v²/c²)
Fuel mass needed to accelerate a 1000 kg payload to a given Δv, using the relativistic rocket equation. Y-axis is logarithmic because the numbers span many orders of magnitude. Each line is a different exhaust velocity.
Kinetic energy of a 1 kg object as it approaches light speed. Y-axis is logarithmic. Notice how the Newtonian curve (½mv²) and relativistic curve agree at low speeds, then diverge dramatically. The relativistic KE shoots toward infinity as v → c. Formula: KE = (γ − 1)mc²