Angle Converter

Intro

Convert angles between degrees, radians, gradians, arcminutes, and arcseconds. Choose your starting and target units above.

What this calculator does

Enter one numeric value and choose its unit. An arcminute is 1/60 of a degree, and an arcsecond is 1/60 of an arcminute (1/3,600 of a degree). Select either as a separate unit; the form does not have a combined degrees-minutes-seconds entry.

What are degrees and radians?

A degree is 1/360 of a full turn. A radian measures the angle at a circle's center when the arc length equals the radius. A half turn is 180° = π radians; a full turn is 360° = 2π radians.

How to convert degrees to radians

Multiply the angle in degrees by π / 180: radians = degrees × π / 180. Here π (pi) is approximately 3.14159265.

For a right angle: 90 × π / 180 = π/2 radians, approximately 1.57079633 radians. Enter 90 with degrees selected to try it.

How to convert radians to degrees

Multiply the angle in radians by 180 / π: degrees = radians × 180 / π. For example, (π/2) × 180 / π = 90 degrees.

The input accepts numbers, not symbolic expressions. To try π/2, π, or 2π radians, enter 1.57079633, 3.14159265, or 6.28318531 respectively. These decimal inputs give approximately 90, 180, and 360 degrees; a rounded input can introduce a small difference.

Assumptions and limitations

• Exact π expressions explain the mathematics; the calculator uses stored numeric factors and displays decimal results.
• Display rounding and rounding in an entered value can affect the final digits. Check the precision needed for technical work.

Formula reference

The BIPM SI Brochure defines the radian in Table 4, note (b), and degree, arcminute, and arcsecond relationships in Table 8.

How we explain formulas, assumptions and sources