Circle CalculatorArea, Circumference, Diameter and Radius from Any One Value
Type the radius, diameter, circumference or area, and this free circle calculator works out the other three as you type. You also get answers in terms of π, step by step working, arc and sector results, and a live diagram that labels every measurement.
- Works from any one value
- Working shown
- Arc and sector mode
- No sign-up
Calculate the radius, diameter, circumference and area of a circle
Type in any box. The other three update as you type.
- Radius5 cm
- Diameter10 cm
- Circumference31.4159 cm= 10π cm
- Area78.5398 cm²= 25π cm²
- Arc length5.236 cm
- Sector area13.09 cm²
- Chord length5 cm
- Segment area2.2647 cm²
- Sector perimeter15.236 cm
Step by step working
Using π = 3.14159265 (full precision)
- Diameter
d = 2 × r2 × 5 = 10 cm - Circumference
C = 2 × π × r2 × 3.14159265 × 5 = 31.4159 cm - Area
A = π × r²3.14159265 × 5² = 78.5398 cm²
The same circle in other units
Lengths are in the unit shown. Areas are in that unit squared.
| Unit | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| mm | 50 | 100 | 314.159 | 7,853.98 |
| cm | 5 | 10 | 31.4159 | 78.5398 |
| m | 0.05 | 0.1 | 0.314159 | 0.00785398 |
| km | 5.000e-5 | 0.0001 | 0.00031416 | 7.854e-9 |
| in | 1.9685 | 3.93701 | 12.3685 | 12.1737 |
| ft | 0.164042 | 0.328084 | 1.03071 | 0.0845396 |
| yd | 0.0546807 | 0.109361 | 0.343569 | 0.00939328 |
| mi | 3.107e-5 | 6.214e-5 | 0.00019521 | 3.032e-9 |
Why this circle calculator is different
Most circle calculators ask you to pick a mode, press a button and read a bare number. This one is built around how people really check a circle.
Start from any one value
Radius, diameter, circumference or area: type whichever one you have. There is no mode to choose and no Calculate button. The other three numbers change while you type.
Answers in terms of π
Homework often wants 25π, not 78.54. The circumference and area are shown both ways. You can also type values such as 10pi or 3/4, so exact inputs stay exact.
The π your class uses
Switch between full precision, 3.14 and 22/7 so the answer matches your textbook.
Working you can copy
Every result comes with the formula, the numbers substituted in and the final value, in the order you would write it by hand.
Arc, sector and chord in the same place
Add a central angle in degrees or radians to get the arc length, sector area, chord length, segment area and sector perimeter. The diagram redraws the slice as you drag the slider.
Eight units at a glance
See the same circle in mm, cm, m, km, inches, feet, yards and miles without opening a second converter.
How to use the circle calculator
Pick what to solve
Leave it on Circle for the radius, diameter, circumference and area. Choose Arc and sector if you also have a central angle.
Type the value you know
Click the matching box and type. Decimals, fractions such as 7/8 and multiples of π such as 10pi all work.
Set the unit and precision
Choose the unit of your measurement, the number of decimal places, and whether π is full precision, 3.14 or 22/7.
Read, check and copy
The results, the diagram and the working update at once. Copy one figure, copy everything, or share a link to the same circle.
Circle formulas for radius, diameter, circumference and area
Every circle is fixed by a single number. Once you know one of the four measurements, the formulas below give the other three. Read across the row for the value you have.
| If you know | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| Radius r | r | 2r | 2πr | πr² |
| Diameter d | d ÷ 2 | d | πd | πd² ÷ 4 |
| Circumference C | C ÷ 2π | C ÷ π | C | C² ÷ 4π |
| Area A | √(A ÷ π) | 2√(A ÷ π) | 2√(πA) | A |
Parts of a circle
- Radius
- The distance from the centre to the edge. It is half the diameter.
- Diameter
- The distance across the circle through the centre. It is twice the radius.
- Circumference
- The distance around the edge, also called the perimeter of the circle.
- Area
- The surface inside the edge, measured in square units such as cm² or ft².
- Pi (π)
- The circumference divided by the diameter. It is about 3.14159 for every circle.
Arc length, sector area and chord formulas
- Arc length
L = (θ ÷ 360) × 2πr, orL = rθwith θ in radians.- Sector area
A = (θ ÷ 360) × πr², orA = ½r²θin radians.- Chord length
c = 2r × sin(θ ÷ 2). Half the chord, the radius and the line to the centre form a right triangle, so you can check it with the Pythagorean theorem calculator.- Segment area
- The sector area minus the triangle under the chord:
½r²(θ − sin θ)in radians.
Worked examples
Four common questions, solved the same way the calculator solves them. Press an example chip in the tool to load similar numbers.
Area of a circle from its diameter
A pizza is 12 inches across. Halve the diameter, then square the radius and multiply by π.
r = 12 ÷ 2 = 6 inA = π × 6² = 113.10 in²
Radius from the circumference
A tree trunk measures 157 cm around. Divide the circumference by 2π to get the radius.
r = 157 ÷ (2 × π) = 24.99 cmd = 157 ÷ π = 49.97 cm
Diameter from the area
A round rug covers 3 m². Divide by π, take the square root, then double it.
r = √(3 ÷ π) = 0.977 md = 2 × 0.977 = 1.954 m
Arc length and sector area
A slice has a radius of 5 cm and a central angle of 60°, which is one sixth of the circle.
L = (60 ÷ 360) × 2 × π × 5 = 5.236 cmA = (60 ÷ 360) × π × 5² = 13.09 cm²
Circumference and area chart by diameter
A quick reference for common sizes. The numbers work in any unit: read a diameter of 10 as 10 cm or 10 inches, and the area is in that unit squared.
| Diameter | Radius | Circumference | Area |
|---|---|---|---|
| 1 | 0.5 | 3.14 | 0.79 |
| 2 | 1 | 6.28 | 3.14 |
| 3 | 1.5 | 9.42 | 7.07 |
| 4 | 2 | 12.57 | 12.57 |
| 5 | 2.5 | 15.71 | 19.63 |
| 6 | 3 | 18.85 | 28.27 |
| 8 | 4 | 25.13 | 50.27 |
| 10 | 5 | 31.42 | 78.54 |
| 12 | 6 | 37.70 | 113.10 |
| 14 | 7 | 43.98 | 153.94 |
| 16 | 8 | 50.27 | 201.06 |
| 18 | 9 | 56.55 | 254.47 |
| 20 | 10 | 62.83 | 314.16 |
| 24 | 12 | 75.40 | 452.39 |
| 30 | 15 | 94.25 | 706.86 |
| 36 | 18 | 113.10 | 1,017.88 |
What a circle calculator helps you do
Circles turn up far outside the classroom. Because one value gives you the rest, a single measurement with a tape is usually all you need.
- Check geometry homework. See the formula and each substitution, then compare them with your own working line by line.
- Plan a round patio, pond or fire pit. Get the area for paving or liner and the circumference for edging. For rooms and odd shapes, use the square footage calculator.
- Compare pizza and cake sizes. Area grows with the square of the diameter, so a 14 inch pizza has about 36% more to eat than a 12 inch one.
- Size wheels, pipes and cuts. A 26 inch wheel travels about 81.7 inches per turn, which is its circumference. Switch units with the unit converter or the inches to cm converter.
- Draw arcs for charts and gauges. Turn a percentage into a central angle, then read the arc length and sector area for the slice.
Circle calculator FAQ
How do I find the area of a circle?
Multiply π by the radius squared: A = π × r². For a radius of 5 cm, the area is π × 25 = 78.54 cm². If you only have the diameter, halve it first to get the radius. The circle calculator does both steps for you and shows the working.
How do I find the circumference of a circle?
Multiply the diameter by π, or use C = 2 × π × r with the radius. For example, a circle with a diameter of 10 cm has a circumference of 31.42 cm. Type either value into the circle calculator to see the result straight away.
How do I find the radius from the circumference?
Divide the circumference by 2π. For example, a circumference of 31.42 cm gives 31.42 ÷ 6.2832 = 5 cm. Type the circumference into its box, and the radius, diameter and area appear at once.
How do I find the diameter from the area?
First divide the area by π. Then take the square root to get the radius, and double it: d = 2 × √(A ÷ π). An area of 78.54 cm² gives a radius of 5 cm, so the diameter is 10 cm.
What is the difference between radius and diameter?
The radius runs from the centre of the circle to its edge. The diameter runs from edge to edge through the centre, so it is always twice the radius. If the radius is 5 cm, the diameter is 10 cm.
Which value of pi does the circle calculator use?
By default it uses π to full double precision, which is 3.141592653589793. You can switch to 3.14 or 22/7 when a textbook or exam asks for one of those. The working always shows which value was used.
How do I calculate arc length and sector area?
Find the fraction of the circle that the angle covers, which is θ ÷ 360. Multiply it by the circumference for the arc length, or by the area for the sector area. With a radius of 5 cm and a 60° angle, the arc is 5.236 cm and the sector area is 13.09 cm². Choose Arc and sector in the calculator to get both, plus the chord length.
Can I enter a value in terms of pi or as a fraction?
Yes. Type 10pi or 10π for a circumference of 10π, and use fractions such as 3/4 or 2 1/2 for measurements in inches. The calculator converts them and still shows the answer in terms of π.
Work out any circle in seconds
One measurement is enough. Type a radius, diameter, circumference or area into the circle calculator and read the rest, with the working ready to copy.
Use the circle calculator