Angle Converter

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

Client-side only Nothing stored No account needed
Last verified July 2026

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Direct answer

What does this converter do?

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

  • 1 radian = 57.3 degree · 1 gradian = 0.9 degree · 1 arcminute = 0.01667 degree
  • All conversions route through the degree as the base unit, so every pair of units agrees regardless of which two you enter.
  • Standard factors are shown in the formula panel at the precision the calculator actually uses, so the arithmetic and the panel agree.
45 degrees converted to 0.7854 radians and 50 gradians
45 degrees is exactly pi/4: 0.7854 rad and 50 grad.

Reference factors (angle)

Exact factors in terms of the degree, from BIPM standards:

  • 1 arcsecond = 0.000277778 degree
  • 1 arcminute = 0.0166667 degree
  • 1 gradian = 0.9 degree
  • 1 degree = 1 degree
  • 1 radian = 57.2958 degree
Formula & evidence

How this calculator works

Reviewed 2026-09-20 · BoringToolsKit Editorial Team

Formula

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

Sources

Sources support the method, terminology, or planning context. Editable assumptions remain your responsibility.

Assumptions to verify

  • 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.

Frequently asked 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.

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Cite this tool

BoringToolsKit. “Angle Converter.” boringtoolskit.com/angle-converter/ (reviewed 2026-09-20). Free to reference in articles, syllabi, and answer posts with a link.

Privacy: Inputs and results stay in this browser. Conversion runs locally in your browser; review the output before relying on it.

Worked example: 45 degrees to radians and gradians

Take the default path: enter 45 with 'from' set to degrees. The script multiplies by pi and divides by 180, so radians = 45 * 3.14159265 / 180 = 0.785398, displayed as 0.7854 rad. That is exactly pi/4, a quarter turn.

The page then shows the other two units derived from that one radian value, not recomputed from 45. Degrees: 0.785398 * 180 / pi = 45.0000. Gradians: 0.785398 * 200 / pi = 50.0000. Gradians come out clean here because 45 degrees is one eighth of a full turn and 400 grad / 8 = 50. Try 30 degrees instead: 0.5236 rad, 50 grad, again exact since 30 degrees is one twelfth of a turn.

Now reverse it: enter 2.5 with 'from' set to radians. Degrees = 2.5 * 180 / pi = 143.2394, and gradians = 2.5 * 200 / pi = 159.1549. Both display to four decimals with no rounding error between them, because the converter always routes through radians as the pivot value. A degree input never feeds the gradian branch directly, so there is no double-rounding drift.

Precision limits and where this converter stops

Every output is fixed to four decimal places with toFixed(4). For 1 radian that is fine (57.2958 degrees), but the four-decimal radian field itself loses information at large angles: 359.9999 degrees entered in degrees mode converts to 6.2832 rad, and converting 6.2832 back by hand gives 359.9997, a drift of 0.0002 degrees purely from display rounding. The underlying math is full precision; only what you read off the screen is clipped.

Empty or non-numeric fields fall back to 0 through the Number() and string guards, so a cleared input silently converts 0 instead of warning you. A negative value also passes through unchanged: -90 degrees returns -1.5708 rad, which is valid for signed rotation but wrong if you meant 270 degrees of a compass bearing.

The unit list is fixed at three: degrees (option 0), radians (option 1), gradians (option 2). Surveying contexts that use mils vary by country (6400 NATO mils per turn, 6283.185 in the mathematical milliradian) and none of those map to the 200-per-pi gradian branch, so military mil conversions need a different tool. Turns and arcminutes (1 degree = 60 arcminutes) are likewise out of scope.