Degrees to Radians Calculator

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.

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.

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.

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.

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.

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.

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.

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.