Primary formula
base radians = source value x source radian factor; target angle = base radians / target radian factor.
Unit converter
Angle Converter
Convert common angle units and see exact pi-style labels for common degree-to-radian results.
Last reviewed: July 6, 2026Unit conversion engine v1.1.0
Unit converter
Angle Converter
Convert one value between supported units, then compare the same source value against all units in this dimension.
Decimal.js unit engine
Enter a value and choose Convert to show the result and convert-all table.
Formula and assumptions
Input assumptions
Conversions use the central NexaCalc unit registry. Displayed decimals are rounded after calculation. No external conversion service is queried.
Precision note
Decimal.js is used for unit conversion arithmetic. Intermediate values are not rounded before display formatting.
Unit conversion flow
Validate
Check value syntax, selected dimension and compatible source and target units.
Normalize
Convert the source value to the dimension base unit or special reciprocal/density bridge when needed.
Convert
Convert to the selected target unit, including affine temperature offsets, fuel reciprocal handling or cooking density when needed.
Explain
Display rounded, scientific, visual and convert-all results with unit-system labels.
What is the Angle Converter?
The Angle Converter converts angle units such as radians, degrees, turns, gradians, arcminutes and arcseconds. It uses the central NexaCalc unit registry so constants are shared across the Conversion category rather than copied into each page.
The tool is for unit conversion only. It does not solve physics, engineering, nutrition or finance equations beyond changing a value from one supported unit to another.
How to use the Angle Converter
Enter a value, choose the source unit and target unit, then select Convert. Use Swap to reverse the units, and use the convert-all table to compare the same value across supported units.
The significant-digits control changes display precision only. Internal calculations use Decimal.js with higher precision before formatting.
Formula and definitions
Linear conversions multiply the source value by the source unit's scale to the base unit, then divide by the target unit's scale to the base unit.
Angle conversions include degree, radian, turn, gradian and arc subdivisions, with exact pi labels for common degree-to-radian outputs.
Calculation example
180 degrees equals pi radians, 90 degrees equals pi/2 radians, and 1 turn equals 360 degrees.
The convert-all table repeats the same source value across every supported unit, which makes it easier to compare systems without changing the original input.
Changing significant digits only changes display precision. The conversion is recalculated from the original source value each time.
Supported units
Angle Converter currently supports: radian, degree, turn, gradian, arcminute, arcsecond.
Units are grouped by system where possible so SI, metric, US customary, Imperial, scientific and other definitions stay readable.
Result visual
The visual output appears only after Convert is selected. It compares the entered source value and target result using the actual calculated output rather than showing a static decoration.
For dimensions with special meaning, such as fuel economy, data transfer or cooking measurement, the visual labels explain the interpretation instead of assigning misleading health, quality or performance categories.
Important distinctions
US customary, Imperial, SI, metric, scientific and international units are labelled separately where the names are easy to confuse.
If two units share a familiar name but use different definitions, NexaCalc keeps the unit-system label visible in the selector and convert-all table.
- Radians are dimensionless but used as the SI angle measure.
- Arcminutes and arcseconds are subdivisions of a degree.
- This page does not solve trigonometric functions.
Common use cases
Use the Angle Converter for quick checks, spreadsheet verification, educational examples, product measurements and cross-system documentation.
For workflows that need live market, weather, nutrition or engineering data, use a dedicated calculator that includes those assumptions instead of treating this unit page as a data source.
Precision and rounding
Decimal.js handles the arithmetic so repeating decimals and very small or very large values remain stable before formatting.
Some source standards define exact conversion factors. Other values are conventional approximations, so the page labels references and keeps critical-use warnings visible.
Limitations
Displayed decimal values may be rounded. Verify critical engineering, scientific, medical, commercial or legal measurements independently.
This page does not validate whether a converted number is appropriate for a design, recipe, shipment, laboratory procedure or financial decision.
Frequently asked questions
Does the Angle Converter use a live API?
No. Unit conversions run locally from static definitions in the NexaCalc unit registry.
Are results exact?
Many unit definitions are exact, but displayed decimals are rounded to the selected significant digits. The result also shows scientific notation.
Why does the Angle Converter show a convert-all table?
The table lets you compare the same source value against every supported unit in the dimension without re-entering the number.
Why are some units labelled US or Imperial?
Some names overlap but have different definitions. NexaCalc labels those systems separately to avoid mixing US customary and Imperial units.
Can I convert to every supported unit?
Yes. The convert-all table uses the same input value and shows every unit supported by this converter.
What do significant digits change?
They change how many meaningful digits are displayed. They do not change the stored unit factors or the original input value.
Can I use scientific notation?
Yes. Inputs such as 1e-6 are supported, and you can display results in standard or scientific notation.
Does the visual affect the answer?
No. The visual is a calculated explanation of the output. The numeric result and table come from the same deterministic conversion function.
Can this replace a professional standard?
No. NexaCalc is useful for everyday and educational conversion, but critical work should be verified against the governing standard or instrument.
Are all units in one shared registry?
Yes. The conversion pages use one central registry to keep factors consistent across tools.
References
- BIPM, The International System of Units SI Brochure, 9th edition and updates. Source.
- NIST, Guide for the Use of the International System of Units and unit conversion factors. Source.
- NIST, CODATA and SI exact defining constants for scientific unit context. Source.
- NIST Handbook 44, Appendix C, General Tables of Units of Measurement. Source.
- IEC, binary prefixes for data units such as KiB, MiB and GiB. Source.
- USDA FoodData Central, ingredient-specific nutrition and density context for cooking measurements. Source.
Conversion reference set v1.1 reviewed July 6, 2026.
Educational disclaimer
This calculator provides mathematical results from the values, conventions and methods you enter. Verify important academic, engineering or professional work independently.