Calculator Inputs
Large screens use three columns, then two, then one.Example data table
| Scenario | Inputs | Output |
|---|---|---|
| Proper time | Δt = 10 s, v = 0.8c | Δτ ≈ 6.000000 s, γ ≈ 1.666667 |
| Coordinate time | Δτ = 2 h, v = 0.6c | Δt ≈ 2.500000 h, γ = 1.250000 |
| Velocity from times | Δτ = 3 s, Δt = 5 s | v ≈ 0.800000c, γ ≈ 1.666667 |
| Spacetime interval | Δt = 5 μs, Δr = 900 m | Timelike, Δτ ≈ 4.000000 μs |
Formula used
γ = 1 / √(1 − v² / c²)
Δτ = Δt / γ
Δt = γΔτ
v = c √(1 − (Δτ / Δt)²)
Δτ = √(Δt² − Δr² / c²), where Δr² = Δx² + Δy² + Δz²
This calculator uses c = 299,792,458 m/s. A real proper time exists only for timelike or lightlike event separations.
How to use this calculator
- Select the calculation mode that matches your known variables.
- Enter times, velocity, or displacement values with the appropriate units.
- Choose the output time unit and decimal precision.
- Click Calculate to show the result panel above the form.
- Use the CSV button to export the result table.
- Use the PDF button to save a clean summary sheet.
Why these outputs matter
This page helps compare reference-frame time, moving-clock time, and invariant intervals. It is useful for relativity coursework, thought experiments, spacecraft timing studies, and unit-checked scenario analysis.
The spacetime mode also reveals whether an event pair is timelike, lightlike, or spacelike, which is essential when deciding whether a physically meaningful proper time exists.
FAQs
1. What is proper time?
Proper time is the elapsed time measured by a clock traveling with the object. It is the shortest timelike interval between two events.
2. What is coordinate time?
Coordinate time is the interval measured in a chosen reference frame. It can be longer than proper time when the moving object travels at relativistic speed.
3. Why does time dilation increase with speed?
As velocity approaches light speed, the Lorentz factor grows rapidly. That makes the stationary-frame interval expand relative to the time recorded by the moving clock.
4. Can this calculator use ordinary units?
Yes. You can enter times in several common units and displacements in multiple distance units. The calculator converts everything internally before solving.
5. What happens if velocity equals light speed?
The Lorentz factor becomes undefined for massive objects at exactly light speed. The calculator therefore accepts only values below c for velocity-based modes.
6. What does a spacelike interval mean?
A spacelike interval means the spatial separation dominates the time separation. In that case, no real proper time connects the two events for a material observer.
7. Why solve velocity from two times?
That mode is helpful when you already know the moving-clock reading and the frame reading. It reconstructs the required relativistic speed from their ratio.
8. Are the exports based on the current result?
Yes. The CSV and PDF actions package the values shown in the result table, so the downloaded file matches the latest successful calculation.