Case 1
- Radius
- 5
78.539816
Open with these valuesCircle Area Calculator
78.539816units²
Result: 78.539816 units²πr² for the area, 2πr for the way round. Enter the radius; if you measured across the circle that is the diameter, so halve it first. The table below carries the circumference for the same radii.
Worked examples
How it's calculated
A = π × r²
- StepMeasure the radius — centre to edge.
- StepEnter it in any length unit.
- ResultRead the area in the square of that unit.
What this number means
A circle is completely described by one measurement. Give the radius — the distance from the centre to the edge — and everything else follows, because every circle shares the same constant π. The area, the space enclosed, is π × r²: square the radius first, then multiply by π. The diameter is simply twice the radius, and the circumference, the distance once around the edge, is 2 × π × r. For a radius of 5 that is an area of 78.539816, a circumference of 31.415927 and a diameter of 10. Each answers a different everyday question: the diameter is what you measure across a round table or a pipe, the circumference is the ribbon you would wrap around it, and the area is the surface you cover — dough on a pizza, soil in a round bed, paint on a circular wall. The thing worth noticing is that the area grows with the square of the radius while the circumference grows only in step with it. Double the radius from 5 to 10 and the circumference doubles to 62.831853, but the area quadruples to 314.159265. The caveat that matters most is units. The radius is unit-agnostic, so the answers only mean something if you keep one unit throughout: centimetres in gives centimetres round and square centimetres of area, never a mix. A real object will also differ a little from a perfect flat circle.
One measurement describes the whole circle
Give the radius and area, diameter and circumference all follow, because every circle shares the same constant. Nothing else needs to be measured.
Radius, not diameter
Entering the diameter where the radius belongs makes the area four times too large, because the radius is squared. It is the single most common slip here.
Square first, then multiply
The area is π × r², not (π × r)². Squaring the product instead of the radius overstates the answer by a factor of π.
Commonly misread
Doubling the radius doubles the area.
It quadruples it, because the radius is squared. Doubling the radius only doubles the circumference.
Circumference and area can share a unit.
Circumference is a length and area is a length squared. A radius in centimetres gives a circumference in centimetres and an area in square centimetres.
Reference table
| Radius | Circumference | Area |
|---|---|---|
| 0.5 | 3.141593 | 0.785398 |
| 1 | 6.283185 | 3.141593 |
| 2.5 | 15.707963 | 19.634954 |
| 5 | 31.415927 | 78.539816 |
| 10 | 62.831853 | 314.159265 |
Questions
How do you calculate the area of a circle?
Square the radius and multiply by π. A radius of 5 gives 25π, about 78.54 square units.
I only know the diameter.
Halve it to get the radius. A circle 10 across has a radius of 5 — entering 10 instead would overstate the area fourfold.
What is the circumference?
2πr, the distance once round the edge. For radius 5 that is about 31.42, and the table above lists it for each radius shown.
Sources and last check
Information, not professional advice.