📐 Radians ⇄ Degrees: Calculator

Convert any angle between degrees and radians instantly.

RESULT
3.141593 rad
180° = 3.141593 rad
In Terms of π
1.0000π rad

Converting Between Degrees and Radians

Degrees and radians are two different units for measuring angles. Degrees divide a full circle into 360 equal parts, while radians measure angles based on the radius of a circle — a full circle equals exactly 2π radians (about 6.2832 radians).

Radians = Degrees × (π ÷ 180)
Degrees = Radians × (180 ÷ π)

Common Angle Reference Table

DegreesRadians (π form)Radians (decimal)
0°00
30°π/60.5236
45°π/40.7854
60°π/31.0472
90°π/21.5708
180°π3.1416
270°3π/24.7124
360°2π6.2832

Why Radians Matter

Radians are the standard angle unit in higher mathematics, physics, and programming because they simplify many formulas — for example, the derivative of sin(x) is cleanly cos(x) only when x is measured in radians. Most calculators and programming languages' trigonometric functions expect radians by default.

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❓ Frequently Asked Questions

Why do programming languages use radians instead of degrees?
Mathematical trigonometric functions (sin, cos, tan) are defined most naturally in radians, and many calculus identities only hold cleanly when angles are in radians — so most programming languages and math libraries default to radians.
How many radians are in a full circle?
A full circle equals 2π radians, which is approximately 6.2832 radians — this corresponds to 360 degrees.
What is π (pi) exactly?
Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159265... It's an irrational number, meaning its decimal representation never terminates or repeats.
How do I convert radians to degrees by hand?
Multiply the radian value by 180/π (approximately 57.2958). For example, 1 radian × 57.2958 ≈ 57.30 degrees.
Do I need a calculator's DEG/RAD mode set correctly?
Yes — most scientific calculators have a mode setting (DEG or RAD) that determines how trigonometric functions interpret angle inputs. Using the wrong mode is one of the most common sources of errors in trigonometry problems.

🏆 About This Tool — Accuracy & Trust

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📐 Accuracy Note: This tool uses standard, widely published formulas and guidelines. Results are estimates for informational purposes; for financial, medical, or engineering decisions, consult a licensed professional.

📅 Last Updated: September 2026.