Degrees to Radians Calculator

Enter an angle in degrees and get the equivalent value in radians — both as a decimal and as a fraction of π. The Degrees to Radians Calculator also shows the complementary and supplementary angles, so you can visualize related angle relationships at a glance. Works with positive and negative values, including decimals. Also try the Sine Calculator (sin).

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Enter any angle in degrees. Decimals and negative values are supported.

Choose how many decimal places to display in the result.

Results

Radians (Decimal)

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Radians (as fraction of π)

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Complementary Angle (90° − θ)

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Supplementary Angle (180° − θ)

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Input Angle (Degrees)

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Results Table

Frequently Asked Questions

How do you convert degrees to radians?

Multiply the angle in degrees by π/180 (approximately 0.01745329). For example, 90° × π/180 = π/2 ≈ 1.5708 radians. This works because a full circle is 360° and also 2π radians, so the conversion factor is π/180. See also our Secant (sec).

What are radians?

A radian is the angle subtended at the center of a circle by an arc whose length equals the radius of that circle. There are 2π radians in a full circle (360°), making 1 radian approximately 57.296°. Radians are the standard unit of angular measure in mathematics and physics.

What are degrees?

A degree is a unit of angular measurement equal to 1/360 of a full rotation. The 360-degree system is believed to have originated with the Babylonians and has been used for thousands of years in navigation, astronomy, and geometry.

How many radians are in a full circle?

A full circle contains exactly 2π radians, which is approximately 6.2832 radians. This is because the circumference of a circle is 2πr, and when the arc length equals the full circumference, the angle sweeps 2π radians. You might also find our Arctan (Inverse Tangent) useful.

What is the formula for degrees to radians as a fraction of π?

Divide the angle in degrees by 180 to get the coefficient of π. For example, 60° ÷ 180 = 1/3, so 60° = π/3 radians. This fraction form is often preferred in mathematics because it expresses the exact value without rounding.

Can I convert negative degrees to radians?

Yes. Negative angles simply indicate a clockwise rotation rather than counterclockwise. Apply the same formula: multiply the negative degree value by π/180. For example, −45° × π/180 = −π/4 ≈ −0.7854 radians.

What is a complementary angle?

Two angles are complementary if they add up to 90°. So the complementary angle of θ is (90° − θ). For example, the complement of 30° is 60°. This calculator shows the complementary angle alongside the degree-to-radian conversion.

What is a supplementary angle?

Two angles are supplementary if they add up to 180°. The supplementary angle of θ is (180° − θ). For example, the supplement of 45° is 135°. Supplementary angles appear frequently in geometry, especially with parallel lines and transversals.