Angle Converter

Last updated: June 2026

Value

deg

From unit

Degrees

90 deg

Radians

1.57079633 rad

Gradians

100 grad

Turns

0.25 turn

Minutes of arc

5,400 arcmin

Seconds of arc

324,000 arcsec

Milliradians

1,570.7963 mrad

Formula

360 degrees = 2 pi radians = 400 gradians = 1 turn. 1 degree = 60 arcmin = 3,600 arcsec.

Angle reference

Angle	Degrees	Radians	Gradians
Full turn	360	2 pi	400g
Half turn	180	pi	200g
Right angle	90	pi/2	100g
45 degrees	45	pi/4	50g
30 degrees	30	pi/6	33.33g

About this calculator

Angle Converter helps you convert angle units to degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians quickly without doing the arithmetic by hand. It is designed for everyday checks where a clear answer matters: trigonometry, navigation, surveying, geometry checks. Enter a number in either side of the converter, use the swap button when you want to reverse direction, then compare the result with the quick reference table. Radians are common in mathematics and programming, while degrees are easier for everyday angle descriptions.

Angle Converter formula

The calculator applies a fixed unit conversion factor. For bidirectional conversion, the reverse formula uses the same factor in the opposite direction.

360 degrees = 2 pi radians = 400 gradians = 1 turn
1 degree = pi / 180 radians = 60 arcminutes = 3,600 arcseconds

How to use the angle converter

Type the angle units value into the first input.
Read the converted degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians value in the second input.
Type into the second input if you want to convert in the opposite direction.
Use the swap button to change which unit appears first.
Check the formula display if you need to show your working.
Use the reference table for common values without repeated typing.

Worked examples

Example conversion

Input: 90 degrees

Calculation: 90 degrees = pi / 2 radians = 100 gradians

Result: 100 gradians

Second example

Input: 1 radian

Calculation: 1 radian = 180 / pi = 57.296 degrees

Result: 57.296 degrees

When this conversion is useful

Use this converter when information is given in angle units but your form, plan, recipe, product listing, or comparison needs degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians. It is especially useful when mixing UK, metric, and imperial measurements.

Trigonometry: Enter the source value, check the converted result, and keep enough decimal places for the level of precision needed.
Navigation: Enter the source value, check the converted result, and keep enough decimal places for the level of precision needed.
Surveying: Enter the source value, check the converted result, and keep enough decimal places for the level of precision needed.
Geometry checks: Enter the source value, check the converted result, and keep enough decimal places for the level of precision needed.

Rounding and precision

The live converter keeps useful decimal precision, while the reference table rounds values for readability. For casual use, rounded values are usually enough. For engineering, legal documents, medical records, building work, or purchase specifications, keep the original units and confirm the required precision before relying on a rounded number.

Common mistakes

Rounding too early and then using the rounded number in another calculation.
Mixing UK imperial and US customary units where they are not the same.
Entering a combined value in one field when the calculator expects separate units.
Copying a result without the unit label.
Using an approximate mental conversion when an exact factor is needed.

Conversion disclaimer

This converter is for general information and everyday calculation support. It does not replace professional measurement, medical, engineering, legal, or product-specific guidance where exact tolerances matter.

Reference table values may be rounded.
Source measurements can be approximate before they reach the calculator.
Some industries require specific rounding rules or certified measuring equipment.

Frequently asked questions

What is the formula for the angle converter?

Use 360 degrees = 2 pi radians = 400 gradians = 1 turn. To convert back, use 1 degree = pi / 180 radians = 60 arcminutes = 3,600 arcseconds.

Can I type in either input?

Yes. The converter is bidirectional, so changing either input updates the other side.

Why does my result have decimals?

Many unit conversions do not produce a whole number. Decimals keep the result more accurate than rounding to the nearest whole unit.

Should I round the answer?

For everyday use, rounding to one or two decimals is often fine. For technical work, keep more decimal places and follow the rounding rule required for that task.

Are UK and US units always the same?

No. Some units, especially gallons and fluid ounces, differ between UK imperial and US customary systems. Use the converter that matches the system you need.

Related calculators

Degrees to Radians Calculator
Radians to Degrees Calculator
Trigonometry Calculator
Triangle Calculator

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.