What is proper time?
The time measured by a clock that is present at both events (start and end). It is always less than the coordinate time measured by a distant observer.
Time Dilation Calculator
t' = t / √(1 − v²/c²)
Calculate relativistic time dilation. t' = t/√(1−v²/c²) — moving clocks run slow.
Calculate
Enter values above to calculate
How it calculates
1
c = 299,792,458 m/s
2
γ = 1/√(1 − v²/c²)
3
t' = γ × t₀ (dilated time in stationary frame)
Formula
t' = t / √(1 − v²/c²)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| t₀ | Proper time (in moving frame) | s |
| t' | Coordinate time (in stationary frame) | s |
| γ | Lorentz factor = 1/√(1−v²/c²) | — |
| v | Velocity | m/s |
| c | Speed of light | m/s |
How to Use This Calculator
This time dilation calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula t' = t / √(1 − v²/c²) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Astronaut travels at 0.9c for t₀ = 10 s (proper time). How much time passes on Earth?
Step 1: γ = 1/√(1−0.81) = 1/√0.19 ≈ 2.294
Step 2: t' = 2.294 × 10
Answer: t' ≈ 22.9 s on Earth — the astronaut's clock runs slower
Common Mistakes
- The proper time (t₀) is always the SHORTER time — the frame in which both events occur at the same place
- GPS satellites travel at ~14,000 km/h — they need both SR and GR corrections totalling ~38 μs/day
- At v = 0.1c, γ ≈ 1.005 — only 0.5% effect
Related
Frequently Asked Questions
Have we measured time dilation?
Yes — muon decay experiments, atomic clock experiments on aircraft, and GPS corrections all confirm time dilation precisely.