Coterminal Angle Calculator

Coterminal angles are angles that look exactly the same when you draw them, pointing in an identical direction even though the number of degrees is different, and this calculator finds them for you. Two angles are coterminal when they differ by a whole number of full turns, that is, by a multiple of 360 degrees. So 45 degrees, 405 degrees, 765 degrees and minus 315 degrees are all coterminal, because each lands the rotating arm in the same final position. Enter any angle in degrees, large, small, positive or negative, and the calculator returns the smallest positive coterminal angle, between 0 and 360 degrees, a negative coterminal angle, and the value in radians, all updating as you type. The reason this matters is at the heart of trigonometry: because coterminal angles point the same way, they have exactly the same sine, cosine and tangent. That means a messy angle like 1080 degrees or minus 200 degrees can be replaced by a tidy equivalent between 0 and 360 without changing any result, which makes evaluating trig functions, sketching angles and solving equations far simpler. It is a core skill in NCEA and senior trigonometry, where angles often run beyond a full circle or swing negative, and where reducing them to a standard range is the first step in many problems. The calculator does the divide-and-take-the-remainder step for you, which is exactly where students often slip, especially with negative angles. Watching the positive and negative coterminal angles update as you change the input also builds a clear mental picture of how angles wrap around the circle. The formula and a worked example are explained clearly below.

Calculate.co.nz is proud to be partnered with Health Based Building, a leader in sustainable and health-conscious building innovation. With over a century of experience, they develop high-performance systems like Foreverbreathe Specification, Magnum Board, and Foreverbreathe Paints to support energy-efficient, non-toxic living environments. Their commitment to healthier homes aligns with our belief that informed choices lead to better outcomes for Kiwi households.