How do I find the diameter from the circumference?

Divide the circumference by pi (approximately 3.14159). The formula is d = C / pi. For example, a circle with a circumference of 31.416 cm has a diameter of 31.416 / 3.14159 = 10 cm. This works in any unit: millimetres, centimetres, metres, inches, or feet, as long as the circumference and diameter are in the same unit.

What is the relationship between circumference, diameter, and radius?

The circumference C of a circle equals pi times the diameter d: C = pi x d. The diameter is twice the radius (d = 2r), so C = 2 x pi x r as well. To reverse this: d = C / pi and r = C / (2 x pi). All three measurements are proportional to each other through pi.

Can I also get the area from the circumference?

Yes. First find the radius r = C / (2 x pi), then calculate the area as A = pi x r squared. This calculator does both steps automatically. For example, a circumference of 62.832 cm gives a radius of 10 cm and an area of 314.159 square centimetres.

Circumference to Diameter Calculator

Enter the circumference of a circle to find its diameter, radius, and area instantly. The formula is d = C / π (diameter equals circumference divided by pi). Works in any unit: mm, cm, m, inches, or feet.

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.

Calculate.co.nz partner: Health Based Building

Standard formula d = C / π | r = C / (2π) | A = πr²

1. Circumference

Circumference (C)

Unit

Decimal places

2. Result

Diameter (d = C / π)

Radius (r = C / 2π)

Area (A = πr²)

cm²

Circle Measurements

Circumference

Input value

Diameter
-
d = C / π

Radius

r = C / 2π

Area

A = πr²

Step-by-Step Calculation

Circumference (C)-

Pi (π)3.14159265358979

Diameter = C / π-

Radius = C / 2π-

Area = π × r²-

Unit-

Worked Example (Default)

Circumference31.416 cm

Diameter = 31.416 / π10.000 cm

Radius = 31.416 / (2π)5.000 cm

Area = π × 5²78.540 cm²

Diameter10.000 cm

How to Convert Circumference to Diameter

The circumference of a circle is the distance around its edge. The diameter is the distance from one side of the circle straight through its centre to the other side. These two measurements are always related by the mathematical constant pi (π = 3.14159...):

C = π × d ⇒ d = C / π

To find the diameter from the circumference, you simply divide the circumference by pi. To find the radius, divide by 2π (or halve the diameter). The area then follows from A = πr².

Formula Reference

What you want	Formula	Example (C = 31.416 cm)
Diameter	d = C / π	31.416 / 3.14159 = 10.000 cm
Radius	r = C / (2π)	31.416 / 6.28318 = 5.000 cm
Area	A = πr²	π × 5² = 78.540 cm²

Common Applications

Pipe and tube sizing: Measuring the circumference of a pipe with a tape measure is often easier than measuring its diameter directly. Divide by pi to get the outer diameter.
Tree and post diameters: Wrap a tape around a tree trunk or fence post to measure circumference, then calculate the diameter to determine timber volume or post fit.
Wheel and tyre sizing: Knowing a wheel's circumference lets you calculate the diameter and confirm the correct tyre fit.
Engineering and manufacturing: Round stock, shafts, and circular flanges are sometimes measured at their perimeter; converting to diameter is a routine step.
Astronomy: The equatorial circumference of Earth is approximately 40,075 km, giving a diameter of 40,075 / π = 12,756 km.

Unit Notes

The circumference and diameter will always be in the same unit. Area will be in that unit squared. For example, a circumference in centimetres gives a diameter in centimetres and an area in square centimetres (cm²). This calculator supports millimetres, centimetres, metres, inches, and feet.

Quick Reference: Circumference to Diameter

Circumference	Diameter	Radius	Area
3.142 cm	1.000 cm	0.500 cm	0.785 cm²
6.283 cm	2.000 cm	1.000 cm	3.142 cm²
15.708 cm	5.000 cm	2.500 cm	19.635 cm²
31.416 cm	10.000 cm	5.000 cm	78.540 cm²
62.832 cm	20.000 cm	10.000 cm	314.159 cm²
314.159 cm	100.000 cm	50.000 cm	7,853.982 cm²

Related Calculators

Maths and Stats Calculators: browse all maths tools.
Circumference Calculator: calculate circumference from diameter or radius.
Area of a Circle Calculator: find circle area from radius or diameter.
Arc Length and Sector Area Calculator: arc and sector calculations.
Annulus Calculator: the area between two concentric circles.

Method: Standard circle geometry. Formula d = C / π is exact for an ideal circle (Euclidean geometry). Pi is taken as 3.14159265358979 (15 significant figures) for all calculations.

This calculator uses exact circle geometry. Results are rounded to the number of decimal places you select. For physical measurements, the accuracy of your result depends on the precision of the circumference you measure.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland via SiteHost new Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-07-02 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.