Circumference Calculator
Circumference of a circle from its diameter or the other way round, with the radius, the area and the arc of one degree shown alongside.
With diameter 10 ft, circumference comes to 31.416 ft — circumference. It is reached in 5 steps, the last of which is pi * diameter, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.
Formula and sources checked · How we check
Diameter 10 ft
31.416 ft
Circumference for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Radius
diameter / 25 ft- Circumference
pi * diameter31.416 ft- Area enclosed
pi * pow(radius, 2)78.54 sq ft- Arc length of one degree
circumference / 3600.087 ft- Circumference in inches
circumference * 12376.991 in
Worked example
A 10 ft circle measures 31.416 ft around and encloses 78.54 sq ft. One degree of that arc is 0.087 ft, or just over an inch — which is how much a mark moves for each degree you are out when laying out a curve.
How to work it out yourself
- 1.Measure straight across the widest point for the diameter.
- 2.Multiply by π. That is the circumference; nothing else is needed.
- 3.To go the other way, divide a measured circumference by π to recover the diameter.
- 4.For the area, halve the diameter and multiply π by that squared.
The formula
- Radius
diameter / 2 - Circumference
pi * diameter - Area enclosed
pi * pow(radius, 2) - Arc length of one degree
circumference / 360 - Circumference in inches
circumference * 12
Source: Wolfram MathWorld — circumference, NIST Digital Library of Mathematical Functions
Questions people actually ask
- How do I get the diameter from a tape around the object?
- Divide the measured circumference by π. A 31.4 ft tape reading is a 10 ft diameter, and this is the reliable way to size a tree or a tank you cannot measure across.
- Is π ever exactly 22/7?
- No. 22/7 is 3.142857, which is high by about 0.04%. It is close enough for a rough layout and wrong for anything machined.
Related
- Circle CalculatorArea, circumference and radius of a circle from its diameter — in square feet and square inches.
- Tank & Cylinder Volume CalculatorVolume of a cylinder in cubic feet, US gallons and litres — round tanks, pools, culverts and post holes.
- Diagonal & Rafter Length CalculatorHypotenuse of a right triangle in feet and inches — brace lengths, rafter runs, and squaring a layout.
- Arc Length and Sector Area CalculatorArc length, sector area, chord and sector perimeter from a radius and an angle, with the fraction of the full circle shown as its own step.
- Semicircle CalculatorArea and perimeter of a half circle from its diameter — and the perimeter is the part people get wrong, because it includes the straight edge.
- Slope & Grade CalculatorGrade percentage, angle in degrees, ratio and roof pitch from a rise and a run.
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