Skip to content
Calcapedia
Menu
Math

Circle Calculator

Know one measurement of a circle? Enter its radius, diameter, circumference or area and get the other three.

Level: Grade 7

  • Common Core standard 7.G.B.4Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Printable worksheet

Circle Calculator

Know the answer you need? Pick an input to work backward.

Inputs
I know the

Result

Area

78.5398 square units

A circle with radius 5 has diameter 10, circumference 31.4159 and area 78.5398.

Radius
5
Diameter
10
Circumference
31.4159

See the step-by-step solution ↓

Step-by-step solution

  1. Find the diameter (d), the distance straight across: it's twice the radius

    d=2×5=10

  2. Find the circumference (C), the distance around: 2 × π × the radius

    C=2×π×5=31.415927

  3. Find the area (A), the space inside: π × the radius × the radius

    A=π×52=78.539816

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Know one measurement of a circle? Get the other three in a moment. A whole circle is set by just one length. The radius is the distance from the center to the edge. Once you know it, everything else follows from fixed formulas that use π (pi, about 3.14). That includes the diameter, the distance around (circumference) and the space inside (area). So any one of the four is enough to find the rest.

Choose the measurement you have and type it in. The calculator turns it into a radius first and then works out the others. It shows each formula with your numbers, so you can follow along.

Where it's used

Why this math matters outside the classroom:

  • Edging a pond. A round pond with a 3 m radius needs 2π × 3, about 18.8 m, of edging to go around it.
  • Pizza sizes. A 16-inch pizza has π × 8², about 201 square inches, nearly twice the 113 square inches of a 12-inch pizza.
  • Bike wheels. A bike wheel 26 inches across rolls about 81.7 inches, its circumference, with each full turn.
  • Lawn sprinklers. A sprinkler that throws water 5 m in every direction waters π × 5², about 78.5 m², of lawn.
  • Round tables. Event planners allow about 2 ft of edge per guest, so a round table 5 ft across, with a 15.7 ft edge, seats about 7.

Grade level and standards: Grade 7; Common Core State Standards for Mathematics 7.G.B.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Select the measurement you know: radius, diameter, circumference or area.
  2. Enter its value. Any length unit works. If you enter an area, use the matching square unit.
  3. Read the other measurements. The main result is the area, or the radius if you started from the area.

What the inputs mean

Circumference (C)
The distance all the way around the edge. It's what you'd measure by wrapping a tape around a pipe or tree trunk.
Area (A)
The space inside the circle, in square units. Entering 50 cm² gives a radius in cm.

Formula and method

d = 2r
C = 2πr = πd
A = πr²
r = d ÷ 2 = C ÷ 2π = √(A ÷ π)

In the formulas, r is the radius, d is the diameter, C is the circumference and A is the area. The symbol √ means square root, and r² means r × r. π (about 3.14159) is how many times the diameter fits around any circle's edge. The circumference grows in step with the radius, but the area grows with the radius squared. So doubling the radius doubles the circumference but makes the area four times as big.

The last line turns the first three around, to get the radius back from whichever value you know. Everything else is then worked out from that radius, using π at full precision.

Worked example

You wrap a tape measure around a round table top and read 100 cm. How big is the table?

  1. Start from the circumference: r = C ÷ 2π = 100 ÷ (2 × π) ≈ 15.9155 cm.
  2. Diameter: d = 2 × 15.9155 ≈ 31.831 cm.
  3. Area: A = π × 15.9155² ≈ 795.7747 cm².

Result: The table has a radius of about 15.9155 cm, a diameter of about 31.831 cm and a surface of about 795.7747 cm².

Understanding the result

Circumference and diameter are lengths, in the unit you entered. Area is in that unit squared. A circle 10 cm across covers about 78.5 cm², not 78.5 cm.

Area depends on the radius squared. So a small error in a measured circumference becomes about twice as big, as a percentage, in the area.

Assumptions and limitations

  • The shape is a true circle.
  • The value you enter is exact. Results are rounded only on screen.
  • It doesn't convert units. If you need to, change lengths or areas first with the length or area converter.
  • Ovals (ellipses), parts of the edge (arcs) and pie-slice shapes (sectors) need their own formulas.

Frequently asked questions

What's the difference between radius and diameter?

The radius runs from the center to the edge. The diameter runs straight across through the center, so it's always exactly twice the radius.

Which value of π does the calculator use?

It uses the full value a computer can store, about 3.141592653589793. So results are more accurate than working by hand with 3.14 or 22/7.

How do I measure the diameter of something I can't cut through?

Measure the circumference with a flexible tape and enter that instead. The calculator divides by π to give you the diameter.

Why is the area unit squared?

Area counts how many little unit squares fit inside the circle. A radius in meters gives an area in square meters.

How this calculator is checked

Method: Standard circle relations C = 2πr and A = πr². The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Circle Calculator on your own website or blog for free. Paste this code where you want it to appear: