How do you convert degrees to radians?

Multiply the degree measure by π/180. For example, 60° × π/180 simplifies to π/3 radians. This is the exact form most trigonometry classes prefer because it keeps π instead of rounding.

How do you convert radians to degrees?

Multiply the radian measure by 180/π. For example, π/4 radians equals 45°. If the radian value is entered as a decimal, the calculator gives a decimal degree answer.

Why are radians used in trigonometry?

Radians connect angle measure directly to arc length. Because many formulas in calculus, trigonometry, and physics use arc length, angular velocity, or circular motion, radians make those formulas cleaner.

Is π radians equal to 180 degrees?

Yes. A half-turn is 180 degrees, and the same angle is π radians. A full turn is 360 degrees or 2π radians.

Education

Radian to Degree Calculator

Convert degrees to radians and radians to degrees, with exact π-form notes, decimal answers, and common angle examples. This page is written for students who need both a fast answer and a clear explanation of the method, so it includes the formula, steps, examples, common mistakes, and practical notes.

Degrees and radians are two ways to measure the same angle

Degrees divide a full turn into 360 parts, while radians measure an angle using the relationship between arc length and radius. The OpenStax angles lesson explains radian measure through the formula that connects central angle, radius, and arc length. This calculator converts both ways and shows the formula so students can understand the step rather than just copy a number.

Conversion formulas

Degrees to radians: radians = degrees × π ÷ 180 Radians to degrees: degrees = radians × 180 ÷ π Examples: 180° = π radians 90° = π/2 radians π/6 radians = 30°

If your class expects exact answers, keep the π form. If the problem is numerical, use the decimal radian value.

Common questions

Multiply the degree measure by π/180. For example, 60° × π/180 simplifies to π/3 radians. This is the exact form most trigonometry classes prefer because it keeps π instead of rounding.
Multiply the radian measure by 180/π. For example, π/4 radians equals 45°. If the radian value is entered as a decimal, the calculator gives a decimal degree answer.
Radians connect angle measure directly to arc length. Because many formulas in calculus, trigonometry, and physics use arc length, angular velocity, or circular motion, radians make those formulas cleaner.
Yes. A half-turn is 180 degrees, and the same angle is π radians. A full turn is 360 degrees or 2π radians.