Angles get measured differently depending on the field, degrees in everyday use and navigation, radians throughout mathematics and physics, gradians in surveying, and arcminutes or arcseconds wherever fine precision matters, like astronomy. This angle conversion calculator converts between all of them instantly, with a swap button and a full breakdown of the math for every conversion.

How to use this angle conversion calculator

1. Enter an Amount.
2. Select the unit you’re converting From.
3. Select the unit you’re converting To.
4. Use the swap button to instantly reverse your From and To units.
5. Click Convert.
6. Review your converted result and the calculation breakdown.
7. Try a preset example to see the calculator in action.

What this angle conversion calculator does

Every supported angle unit converts through a common base, typically degrees or radians, with your input value converted to that base first, then converted again into your target unit. This two-step approach is what allows direct conversion between any two supported units, whether you’re converting a navigation bearing in degrees into radians for a trigonometric calculation, or checking a surveying angle in gradians against a more familiar degree value.

Common angle units and where they’re used

The core conversion relationships

Radians are defined directly from the geometry of a circle (the ratio of arc length to radius), which is why they’re the natural unit throughout calculus and physics, trigonometric derivatives and many physics formulas only take their simplest form when angles are measured in radians rather than degrees.

Why gradians exist alongside degrees

Gradians were designed specifically to make right angles and percentage-based grade calculations simpler: a full circle is exactly 400 gradians, meaning a right angle is exactly 100 gradians, a quarter-circle is 100, and so on in clean round numbers. This made gradians popular historically in surveying and some engineering disciplines, particularly across parts of Europe, even though degrees remain the more universally recognized unit for everyday use.

Arcminutes and arcseconds: precision below a whole degree

When a measurement needs to be more precise than a whole degree allows, arcminutes and arcseconds subdivide it further, the same way minutes and seconds subdivide an hour. This matters most in fields like astronomy, where the apparent size or position of an object in the sky often needs to be specified far more precisely than a single degree can capture, arcseconds are commonly used for exactly this kind of fine angular measurement.

Using the swap button

Rather than manually re-selecting both dropdowns to reverse a conversion, the swap button flips your From and To units in one click and immediately recalculates, useful for quickly checking a conversion in both directions without retyping anything.

Frequently asked questions