Annulus Calculator

An annulus is the mathematical name for a ring: the flat, donut-shaped region trapped between two circles that share the same centre. You meet annulus shapes far more often than the unusual name suggests, from washers, O-rings and pipe cross-sections to garden borders, running tracks, CDs and the cross-section of any tube or pipe. This calculator works out everything you usually need to know about one from just two measurements, the outer radius and the inner radius. Enter those and it instantly returns the area of the ring, the width of the ring (the distance across it), and both the outer and inner circumferences, all in matching units. The area is the figure people reach for most, because it tells you the amount of material in a washer, the cross-sectional area of a pipe wall, or the paved surface of a circular path, and it is found neatly by taking the area of the big circle and subtracting the area of the small hole in the middle. The calculator handles that for you and updates the moment you change a value, so you can size a ring to a target area by trying different radii, or check the material in a part you are machining or ordering. It is a genuinely useful tool for engineers, machinists, builders, landscapers, makers and students alike, removing the small but error-prone arithmetic of squaring radii and multiplying by pi twice over. Below the calculator you will find the exact formulas, an explanation of why the area is a simple subtraction of two circles, and a clear worked example so you can understand the method and apply it confidently by hand whenever you need to.

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.