What this calculator does
Length contraction works out how much shorter a fast-moving object appears along its direction of motion. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormulaL = L₀√(1−v²/c²) (special relativity, c = 299,792,458 m/s)
The inputs explained
| Field | What to enter |
|---|---|
| Proper length (at rest) (m) | A number, measured in m. Starts at 100. |
| Relative speed (m/s) | A number, measured in m/s. Starts at 150000000. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with proper length (at rest)
Every other input is held at the calculator’s starting values while proper length (at rest) varies. Select any row to load that scenario into the calculator.