How this instrument works
Triangle angles computed during calculus or physics work often come out in radians, the unit built from a circle's own arc length rather than an arbitrary 360-part split — but reading a triangle's actual shape is usually far more intuitive in degrees, the everyday unit most people already have a feel for. Converting between them is a straightforward scaling: multiply the radian measure by 180⁄π.
This conversion doesn't change the angle itself in any way — a triangle's corner is exactly as sharp or as wide regardless of which unit describes it, exactly the way a distance stays the same whether it's measured in miles or kilometers.
This page is the reverse direction of this site's Trig Degree calculator, which instead converts FROM degrees INTO radians — together, the two pages cover both directions of the identical unit conversion.
- Enter the angle in radians into the Angle in radians field.
- Read Angle in degrees: the same angle, converted to the more familiar unit.
- Try π (about 3.14159) to see it convert to exactly 180°, a straight angle.
Worked example — π⁄3 radians
A triangle's interior angle measured as π⁄3 radians converts to exactly 60° — a common angle in an equilateral or 30-60-90 triangle, now expressed in the more everyday unit.
π⁄2 radians converts to exactly 90°, a right angle. π radians converts to exactly 180°, a straight angle — the sum of an entire triangle's three interior angles.
Questions
How do you convert radians to degrees?
Multiply the radian measure by 180 divided by π — a fixed scaling factor that converts between the two units without changing the angle itself in any way.
Why are triangle angles sometimes given in radians?
Radians arise naturally from a circle's own arc length rather than an arbitrary split into 360 parts, making them the preferred unit throughout calculus, physics, and most higher mathematics — even when the final answer is more intuitively read in degrees.
How is this different from the Trig Degree calculator on this site?
This page converts FROM radians INTO degrees; that page runs the identical conversion in the opposite direction, from degrees into radians.
What angle does π radians represent?
180° exactly — a straight angle, which happens to also be the total sum of any triangle's three interior angles combined.
Does converting units change the actual angle?
No — a triangle's corner is exactly as sharp or as wide regardless of which unit describes it, the same way a physical distance doesn't change whether it's read in miles or kilometers.