# Angle Converter

> Angle converter that switches between degrees, radians, gradians, turns, arcminutes, and arcseconds instantly. Free, private, runs in your browser, no signup.

- **Canonical URL:** https://boringtoolskit.com/angle-converter/
- **Category:** Converters
- **Evidence level:** authored-methodology
- **Reviewed:** 2026-09-20
- **Last verified:** 2026-10-12
- **Privacy:** Inputs and results stay in this browser unless the page clearly labels an external request.

## How it works

Converts through radians first: degrees x PI/180, radians unchanged, gradian x PI/200, then back out as radians x 180/PI (degrees) or radians x 200/PI (gradians). Here PI = 3.141592653589793, so 180 degrees = PI radians = 200 gradians.

## Worked example

1 radian = 57.3 degree · 1 gradian = 0.9 degree · 1 arcminute = 0.01667 degree

## Assumptions

- Inputs are treated as exact decimal values.
- Standard (not historical or survey) unit definitions are used.
- The calculation uses the factors at the precision shown in the formula panel; rounding beyond that is display-only and adds no accuracy.

## Common questions

### Why convert through degree instead of directly?

Routing every unit through a single base (degree) means each unit needs only one exact factor against the standard, and any pair combines cleanly. Direct pair factors drift apart over time in hand-maintained tables; a base-unit graph cannot.

### Where do these exact factors come from?

From published standards (BIPM: SI Brochure, plane angle units). Units like the inch are defined exactly (1 in = 2.54 cm since 1959), so conversions between standard units are exact, not approximate.

### How precise is the converted angle?

The conversion applies the standard factors shown in the formula panel. The practical limit is your input: the result only regroups the number you entered, so digits beyond what you actually measured do not add accuracy. 3-4 significant figures usually matches what the source measurement knew.

## Sources

- [SI Brochure, plane angle units](https://www.bipm.org/en/publications/si-brochure)

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