Degrees to Radians Converter

How to use the degrees to radians calculator

What this calculator does

This converter expresses the same plane angle in degrees and radians. It uses the exact identity 360° = 2π rad, so the conversion itself is mathematical rather than an estimate. The decimal display is rounded for readability, while the internal value and exported workbook retain full JavaScript numeric precision. The tool does not determine an angle from side lengths, coordinates, or a diagram; it only changes the unit used to express an angle you already know.

When to use it

Use it when preparing trigonometry or calculus work that expects radians, converting a geometry result stated in degrees, checking a programming or engineering input that uses radians, or translating a rotation used in graphics, robotics, navigation, or physics. Radians are the coherent SI unit for plane angle, as explained in the NIST guidance on plane angles and radian – degree conversion.

How to calculate

1. The calculator opens with a complete demonstration: 90 degrees and π/2 radians. The matching Excel workbook is immediately available.
2. Replace the value in Degrees to convert degrees to radians, or replace the value in Radians to convert radians to degrees. The field you edit most recently becomes the source.
3. Read the decimal result, exact multiple of π, reverse conversion, and formula in the Live result panel. The summary pills repeat the current values for quick scanning.
4. Select Download Excel to create a fresh workbook from the current valid inputs and outputs. Select Reset to clear both angle fields and all calculated content; export then remains disabled until a complete valid value is entered again.

Input guide

Degrees accepts a required finite decimal number in degree units when that field is the one being edited. Examples include 90, 22.5, 360, and -45. A decimal point is the supported separator; scientific notation, thousands separators, degree symbols inside the box, and decimal commas are rejected to prevent ambiguous interpretation. Positive and negative angles are valid because direction can be represented by sign. Increasing the degree value increases the radian value proportionally. A common mistake is typing “90°” instead of the numeric value 90.

Radians accepts a required finite decimal number in radians when that field is edited. A realistic example is 1.5707963267948966, which equals π/2. Enter decimal radians rather than text such as “pi/2”; the exact π form is calculated and displayed automatically. Negative radians are valid. Increasing the radian value increases degrees proportionally. A common mistake is entering a degree value in this box without first converting it.

Output guide

Radians is the decimal radian result rounded to ten decimal places. Exact multiple of π shows a simplified fraction of π when the value is close to a rational multiple with a modest denominator; otherwise it shows a decimal coefficient times π. Degrees is the same angle in degrees, rounded to ten decimal places. Formula used shows the active conversion path. The three summary pills repeat Degrees, Radians, and the π form. The common-angle table lists fixed identities for 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360°. Zero means no rotation; negative values indicate the opposite orientation under the chosen sign convention. None of these outputs is a recommendation.

Worked example

The startup example uses 90°. Multiply by π/180: 90 × π/180 = π/2. As a decimal, π/2 is 1.5707963267948966, displayed as 1.5707963268 rad. Reversing the calculation gives 1.5707963267948966 × 180/π = 90°. These same typed values appear in the first-open controls, result panel, summary pills, and workbook checkpoints.

Learn more

The BIPM SI Brochure defines the radian as the coherent unit for plane angle. NIST also explains that the conversion follows from 360° = 2π rad in its Guide for the Use of the International System of Units.