Circle Calculator

Enter the radius, diameter, circumference or area – the calculator works out all the other values. Plus annulus, sector and segment, with a diagram and step-by-step solution.

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The circle formulas

  • Circumference: C=2πr=πdC = 2\pi r = \pi d
  • Area: A=πr2A = \pi r^2
  • Radius from circumference: r=C÷2πr = C \div 2\pi
  • Radius from area: r=A÷πr = \sqrt{A \div \pi}

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Enter values

Length unit
What do you know?
cm
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Result

Area A

78.54 cm²

r = 5.00d = 10.00A = 78.54 cm²C = 31.42 cm
Radius rinput
5.00 cm
Diameter d
10.00 cm
Circumference C
31.42 cm

Calculated with π ≈ 3.14

Schools often use 3.14. That gives A = 78.50 cm² – −0.051 % compared with the exact value.

Step-by-step solution

The radius r = 5.00 cm is given, so all other values follow directly.

  1. 1. Diameter

    d=2r=2⋅5.00=10.00 cmd = 2r = 2 \cdot 5.00 = 10.00\,\text{cm}

  2. 2. Circumference

    C=2πr=2π⋅5.00=31.42 cmC = 2\pi r = 2\pi \cdot 5.00 = 31.42\,\text{cm}

  3. 3. Area

    A=πr2=π⋅5.002=78.54 cm2A = \pi r^2 = \pi \cdot 5.00^2 = 78.54\,\text{cm}^2

In other units

Area
7,853.98mm²
78.54cm²
0.79dm²
0.01m²
0.0000785a
0.000000785ha
0.00000000785km²
Length (circumference)
314.16mm
31.42cm
3.14dm
0.31m
0.000314km

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The number π

π=Cd\pi = \frac{C}{d}

π is the ratio of a circle's circumference to its diameter – the same for every circle, whatever its size. A circle with a 1 m diameter has a circumference of 3.14159… m. This calculator works with π to 15 decimal places internally and only rounds for display.

π = 3.14159 26535 89793 23846 26433 83279 50288 …

Around 250 BC Archimedes pinned π down using a 96-sided polygon: between 3 10/71 and 3 1/7, i.e. between 3.1408 and 3.1429. That is where the approximation 22/7 comes from.

π is irrational: its decimals never end and never repeat (proved by Johann Heinrich Lambert in 1761). In 1882 Ferdinand von Lindemann proved that π is also transcendental, which is why “squaring the circle” with compass and straightedge is impossible.

How accurate are the π approximations?

ApproximationValueDeviationError at r = 1 m (area)
3.143.14 school value3.1400000−0.05070 %−15.927 cm²
227\tfrac{22}{7} Archimedes3.1428571+0.04025 %+12.645 cm²
355113\tfrac{355}{113} Zu Chongzhi (5th c.)3.1415929+0.00001 %+0.003 cm²

All circle formulas at a glance

QuantityFormula
Diameterd=2rd = 2r
CircumferenceC=2πr=πdC = 2\pi r = \pi d
AreaA=πr2=πd24A = \pi r^2 = \frac{\pi d^2}{4}
Radius from circumferencer=C2πr = \frac{C}{2\pi}
Radius from arear=Aπr = \sqrt{\frac{A}{\pi}}
Annulus areaA=π(R2−r2)A = \pi\left(R^2 - r^2\right)
Arc lengthb=2πr⋅α360∘b = 2\pi r \cdot \frac{\alpha}{360^\circ}
Sector areaA=πr2⋅α360∘=b⋅r2A = \pi r^2 \cdot \frac{\alpha}{360^\circ} = \frac{b \cdot r}{2}
Chords=2rsin⁡α2s = 2r \sin\frac{\alpha}{2}
Segment areaA=r22(α^−sin⁡α)A = \frac{r^2}{2}\left(\hat{\alpha} - \sin\alpha\right)
Radius from chord and heightr=s28h+h2r = \frac{s^2}{8h} + \frac{h}{2}

Rectangle, triangle, trapezoid or a free-form floor plan? The area calculator covers all other shapes. For cylinders, spheres and cones use the volume calculator.

Go to the area calculator →Go to the volume calculator →

As of: 27 Oct 2026

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Frequently Asked Questions

Use A = π × r². Square the radius and multiply by π ≈ 3.14159. Example: r = 5 cm gives A = π × 25 = 78.54 cm². If you know the diameter, A = π × d² ÷ 4.

Use C = 2 × π × r or, equivalently, C = π × d. A circle with a 10 cm diameter has a circumference of π × 10 = 31.42 cm.

Divide the circumference by π: d = C ÷ π. A tree trunk with a girth of 157 cm therefore has a diameter of about 157 ÷ 3.14159 = 49.97 cm, roughly 50 cm. The radius is r = C ÷ (2 × π).

Divide the area by π and take the square root: r = √(A ÷ π). For A = 1 m² that gives r = 0.5642 m, i.e. a diameter of 1.128 m.

The radius r runs from the centre to the edge, the diameter d straight through the centre from edge to edge. The diameter is therefore always twice the radius: d = 2 × r.

Subtract the area of the hole from the area of the large circle: A = π × (R² − r²). Example: R = 10 cm, r = 6 cm gives π × (100 − 36) = 201.06 cm².

A sector is the share α ÷ 360° of the circle. Arc length b = 2 × π × r × α ÷ 360°, area A = π × r² × α ÷ 360°. A 60° slice of a circle with r = 10 cm has a 10.47 cm arc and an area of 52.36 cm².

A sector is bounded by two radii and the arc – like a slice of cake with its tip at the centre. A segment is bounded by a chord and the arc – like an arch. Its area is the sector's area minus the triangle formed by the two radii and the chord.

Use r = s² ÷ (8 × h) + h ÷ 2. An arch with a 12 cm span (chord s) and a 2 cm rise (height h) has a radius of 144 ÷ 16 + 1 = 10 cm.

For most everyday tasks, yes: 3.14 is only 0.05% off the exact value. For a circle with a 1 m radius that is 16 cm² too little area. 22/7 is 0.04% too high; 355/113 is accurate to six decimal places.

Multiply by π ÷ 180°: 90° = π/2 ≈ 1.5708, 180° = π, 360° = 2π. In radians the arc length becomes particularly simple: b = r × α.

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