The Circumference Calculator takes a circle's radius or diameter and returns the full set: circumference, the other of radius and diameter, and the enclosed area, in your units. One measurement in, every property of the circle out.
How It Works
Give the radius and the calculator doubles it for the diameter, multiplies by pi twice over for the circumference, and squares it with pi for the area. Give the diameter instead and it halves to the radius first. Nothing else about a circle needs measuring: these three constants of proportionality are the whole geometry.
Parameters
| Input | Required | Meaning | |---|---|---| | Radius or diameter | Yes | Either one; the other is derived | | Units | No | Any consistent length unit |
Worked examples
A radius of 7 gives a diameter of 14, a circumference of 43.98, and an area of 153.94 square units. A diameter of 10 gives a radius of 5, a circumference of 31.42, and an area of 78.54. The pair worth memorizing from these: circumference is a little over three times the diameter (pi times, exactly), and doubling the radius quadruples the area, which is why a 14-inch pizza is not twice a 7-inch pizza but four times it, the most practically useful fact in this entire topic.
Where the circumference is the working number
Anything that rolls, wraps, or rotates is specified by circumference wearing a disguise. A wheel's circumference is the distance per revolution, which is how bicycle computers convert wheel turns to distance and why the wheel size setting matters to their accuracy. A belt or chain around two pulleys, the material to edge a round table or a garden bed, the distance around a running track's curved ends, a tree's girth (foresters measure circumference precisely because diameter cannot be measured on a standing tree, then divide by pi), and the waist measurement in health contexts are all circumferences in work clothes. In each case the practical measurement is the wrap, and the calculator's job runs in reverse: from the measured circumference, radius and diameter follow by dividing by 2pi and pi respectively.
Pi, precision, and units
The calculator carries pi to full double precision, so its results are exact to the digits shown; hand calculations with 3.14 or 22/7 introduce errors of about 0.05% and 0.04% respectively, invisible for fencing a garden and relevant for machining. Units need one moment of care: the area comes out in the square of whatever unit the radius used, so a radius in centimetres yields square centimetres, and mixing a diameter in inches with an expectation of square feet is the classic way to be wrong by a factor of 144. Convert the input first, or convert the area by the square of the length conversion.
Common errors
Entering the diameter where the radius belongs doubles the circumference and quadruples the area, the single most frequent circle mistake, and the reason the calculator labels its input unambiguously and shows both values back to you: check that the shown radius and diameter stand in the 2:1 relation to the number you meant. Second is measuring a real object's "diameter" across a chord that misses the centre, which always understates it; measure across the widest span, or measure the circumference with a tape and divide by pi, the surveyor's trick. Third is applying circle formulas to ellipses, whose circumference has no elementary closed form at all; an oval garden needs an approximation formula, not this calculator.
Frequently Asked Questions
How do I get the radius from a measured circumference?
Divide by 2pi (about 6.283). A circumference of 31.42 implies a radius of 5 and a diameter of 10. Equivalently, diameter is circumference divided by pi.
Does the calculator work for a semicircle?
Its outputs describe the full circle. A semicircle's perimeter is half the circumference plus the diameter (pi r + 2r), and its area is half the shown area; the calculator supplies both ingredients.
Why is the area in square units while circumference is not?
Circumference is a length, measured along a line, so it carries the input unit. Area counts unit squares filling the disc, so the unit squares too. The two numbers are never interchangeable, and a result that confuses them is off by a factor of the radius itself.