What this calculator does
The area of a circle is the amount of flat space enclosed inside it, found from A = πr². This calculator leads with that area, worked out from whichever measurement you already have: the radius, the diameter, or the circumference.
Because area and circumference are so often wanted together, whether for a costing sheet, a garden bed or a maths assignment, this page also works out the circumference of a circle from the same input and shows it directly underneath the area, rather than making you run the numbers twice.
The formula
The area of a circle formula is A = πr², so the radius is squared and multiplied by π. If you entered a diameter instead, the radius used is half of it (r = d/2); if you entered a circumference, the radius is worked back out first (r = circumference/2π), and the same A = πr² formula is applied from there.
| Term | Meaning |
|---|---|
| A | Area: the space enclosed inside the circle, πr². |
| r | Radius: the distance from the centre to the edge. |
| π | Pi, approximately 3.14159, the ratio that links a circle’s radius, diameter and circumference to its area. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the radius, diameter or circumference, whichever measurement you already have. |
| This value is the | Select which measurement the value above represents. |
When to use it
Costing a circular surface
Turf, paving, glass, fabric or paint priced per square metre needs the area of circle in question, worked out from whatever measurement (usually a diameter) is easiest to take on site.
Comparing two circular sizes
Doubling a diameter does not double the area, it quadruples it, so working out the actual area of a circle before comparing two sizes avoids a common and costly mistake.
Working from a measured circumference
A tape measure wrapped around a circular object gives the circumference directly; converting that to an area, via the radius, is the more useful figure for a materials estimate.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the area of a circle change with the radius?
The area and circumference of a circle for a range of radius values.
| Radius | Area | Circumference of the circle |
|---|---|---|
| 1 | 3.142 | 6.283 |
| 2 | 12.566 | 12.566 |
| 5 | 78.540 | 31.416 |
| 10 | 314.159 | 62.832 |
| 20 | 1,256.64 | 125.664 |
| 50 | 7,853.98 | 314.159 |
Area of circle from radius, diameter or circumference
A radius-5 circle, entered instead as its diameter and as its circumference, to show the area of circle formula returns the same answer regardless.
| The value entered is the | Area | Radius |
|---|---|---|
| Radius (5) | 78.540 | 5.000 |
| Diameter (5) | 19.635 | 2.500 |
| Circumference (5) | 1.989 | 0.7958 |
Questions
What is the area of a circle formula?
A = πr², the radius squared and multiplied by π. If you only know the diameter, halve it first to get the radius before squaring.
How do you find the area of circle when you only have the diameter?
Divide the diameter by 2 to get the radius, then apply A = πr² as usual. Equivalently, A = π(d/2)², or A = πd²/4.
How is area of a circle different from circumference of a circle?
Area measures the flat space enclosed inside the circle, in square units; circumference measures the length of the boundary around it, in linear units. They are related through the same radius but answer different questions.
Why does area grow faster than circumference as a circle gets bigger?
Circumference is proportional to the radius (2πr), a straight-line relationship, while area is proportional to the radius squared (πr²), so area accelerates away from circumference as the radius increases.
For circumference as the headline figure instead, see the circumference calculator. For every circle measurement from a single input at once, see the full circle calculator.