What this calculator does
Modular exponentiation works out computes baseᵉˣᵖ mod m efficiently using square-and-multiply. 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
FormulaRepeated squaring: result = result × base (mod m) whenever the current exponent bit is 1, halving the exponent each step
The inputs explained
| Field | What to enter |
|---|---|
| Base | A number. Starts at 4. |
| Exponent (non-negative integer) | A number. Starts at 13. |
| Modulus | A number. Starts at 497. |
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 base
Every other input is held at the calculator’s starting values while base varies. Select any row to load that scenario into the calculator.