Skip to content
CalculatorBuddy

Circle Calculator

Find the radius, diameter, circumference, and area of a circle from any one value. Uses D = 2R, C = 2πR, and A = πR².

Maintained by CalculatorBuddy TeamEditorial methodology

Add as a preferred source on Google (opens in a new tab)

Enter the radius R. Diameter, circumference, and area follow from 2R, 2πR, and πR².

ExampleSample values — edit any field to see your result.

Distance from the center to any point on the circle. Must be positive.

Results update as you type.

Diameter (D)

20

Estimated result

Given
Given radius (R) = 10
Radius (R)
10
Circumference (C)
20π ≈ 62.83
Area (A)
100π ≈ 314.16

Saved calculations stay only in this browser. Share copies a link containing your entered values.

Compare scenarios

Keep a baseline, then change an assumption to see its effect side by side.

Calculation steps

Worked solution
Diameter = 2R = 20
Circumference = 2πR = 20π = 62.831853071796
Area = πR² = 100π = 314.15926535898
Diameter (D)20

Enter any one of radius, diameter, circumference, or area and this calculator fills in the rest. A circle is the set of all points in a plane at a fixed distance (the radius) from a center. The same relationships hold in any length unit.

Starting from one value

GivenRadiusDiameterCircumferenceArea
R = 10102020π ≈ 62.831853071796100π ≈ 314.15926535898
R = 551010π ≈ 31.41592653589825π ≈ 78.539816339745
D = 1051010π ≈ 31.41592653589825π ≈ 78.539816339745
C = 10≈ 1.591549430919≈ 3.183098861837910≈ 7.9577471545948
A = 100≈ 5.6418958354776≈ 11.283791670955≈ 35.44907701811100

π is irrational (and transcendental), so circumference and area are usually printed as a short π coefficient plus a 14-significant-digit decimal when you start from R or D.

Examples

Radius 10 (default)

D = 2 × 10 = 20. C = 2π × 10 = 20π ≈ 62.831853071796. A = π × 10² = 100π ≈ 314.15926535898.

Diameter 10

R = 10 / 2 = 5. C = π × 10 = 10π ≈ 31.415926535898. A = π × 5² = 25π ≈ 78.539816339745.

Circumference 10

R = 10 / (2π) ≈ 1.591549430919. D = 10 / π ≈ 3.1830988618379. A = 100 / (4π) ≈ 7.9577471545948.

Area of 100 square units

R = √(100 / π) ≈ 5.6418958354776. D = √(400 / π) ≈ 11.283791670955. C = 2√(100π) ≈ 35.44907701811.

Formula

Radius, diameter, circumference, and area are linked through π, the ratio of circumference to diameter (about 3.14159):

D = 2R
C = 2πR
A = πR²

Solve for the radius when a different value is given, then apply the same three identities:

R = D / 2
R = C / (2π)
R = √(A / π)

Equivalent forms used in the steps:

C = πD
A = π(D / 2)²
A = C² / (4π)
C = 2√(πA)

The Radius tab defaults to R = 10, which gives D = 20, C = 20π ≈ 62.831853071796, and A = 100π ≈ 314.15926535898. The Area tab defaults to 100 square units.

Geometric limits

The formulas describe an ideal Euclidean circle from one exact measurement. A measured diameter, circumference, or area carries uncertainty into every derived value, and displayed digits do not create additional accuracy. Use consistent linear and square units; the calculator does not estimate irregular or elliptical shapes.

Frequently asked questions

What do I need to enter?
Any one positive value: radius, diameter, circumference, or area. The calculator recovers the radius first, then fills in the other three using D = 2R, C = 2πR, and A = πR². Zero and negative numbers are rejected.
What is the difference between radius and diameter?
Radius R is the distance from the center to any point on the circle. Diameter D is the largest distance between two points on the circle and always passes through the center. They are related by D = 2R, so a radius of 10 has diameter 20.
How are circumference and area calculated?
Circumference is the distance around the circle, C = 2πR (or πD). Area is the space inside, A = πR². A radius of 10 is C = 20π ≈ 62.831853071796 and A = 100π ≈ 314.15926535898. π is the ratio of circumference to diameter, about 3.14159.
Can I start from area or circumference instead of radius?
Yes. From circumference, R = C / (2π) and A = C² / (4π). A circumference of 10 has radius ≈ 1.591549430919 and area ≈ 7.9577471545948. From area, R = √(A / π). An area of 100 has radius ≈ 5.6418958354776 and circumference ≈ 35.44907701811.
Do I need to pick units?
Keep one consistent length unit. If R is in centimetres, D and C are in centimetres and A is in square centimetres. This page does not convert between units — use the Area Calculator or Square Footage Calculator when you need square feet, metres, or acres.

Related calculators