Know just one thing about a circle? Pick it, type the value and the calculator gives the radius, diameter, circumference and area together, with each step worked out. A diagram below names the parts of a circle: radius, diameter, chord, arc, sector, tangent and secant.
Choose what you know: radius, diameter, circumference or area.
Type its value.
Read the other three values and follow the steps.
Diameter: D = 2 × r
Circumference: C = 2 × π × r = π × D
Area: A = π × r²
Radius from area: r = √(A ÷ π)
Radius from circumference: r = C ÷ (2 × π)
A circle is fully fixed by one number. If you know its radius, you can work out its diameter, the distance around it and the space inside it, and the same is true starting from any of the other three. The circle calculator does this in one step: choose whether you know the radius, diameter, circumference or area, type the value, and read the rest.
This is useful in class and outside it. A tailor or carpenter usually measures across a round table, which is the diameter. A string wrapped around a pipe or a tree trunk gives the circumference. A plan may state only the area of a round garden. In each case you need to get back to the radius first, and the calculator shows that step clearly before finding the others. A labelled drawing names the parts of a circle for revision.
1. Decide what you know: radius, diameter, circumference or area.
2. Get the radius first. From the diameter, halve it. From the circumference, divide by 2π. From the area, divide by π and take the square root.
3. Diameter = 2 × radius.
4. Circumference = 2 × π × radius.
5. Area = π × radius × radius.
6. Write lengths in the unit you measured and the area in that unit squared.
Measure around any circle and divide by the distance across it, and you always get the same number, a little more than 3. That number is called π, pronounced pi. It is about 3.14159, and its decimals go on for ever without repeating. School problems often use 22/7 or 3.14 because they are close and easy to work with. Indian mathematicians such as Aryabhata gave very accurate values of π more than 1,500 years ago.
Cut a circle into many thin slices like a pizza and arrange the slices side by side, pointing up and down in turn. The shape you get is very close to a rectangle. Its height is the radius r, and its length is half of the circumference, which is π r. Height times length gives π r × r, which is π r². The thinner the slices, the closer the shape gets to a perfect rectangle.
A chord is a straight line joining two points on the circle, and the longest chord, through the centre, is the diameter. An arc is a piece of the curved edge. A sector is a slice shaped like a piece of cake, bounded by two radii and an arc. A tangent is a straight line that just touches the circle at one point, and a secant is a line that cuts through it at two points.
Anita wants to put a lace border around a round table cloth. She measures straight across the cloth through its centre and gets 140 cm. How much lace does she need, and how much cloth was used?
Radius is half the diameter: r = D ÷ 2 = 140 ÷ 2 = 70
Diameter: D = 2 × r = 2 × 70 = 140
Circumference: C = 2 × π × r = 2 × 3.141593 × 70 = 439.822972
Area: A = π × r² = 3.141593 × 70² = 15,393.804003
Answer: Radius 70; Diameter (given) 140; Circumference 439.822972
Using the diameter in A = π r² without halving it first, which makes the area four times too big.
Mixing up the formulas: 2π r is the distance around, π r² is the space inside.
Forgetting to take the square root when finding the radius from the area.
Writing the area in cm instead of cm².
Expecting the same answer as a textbook that uses 22/7, when the full value of π gives a slightly different result.
Finding the length of border, fencing or wire needed to go around something round.
Working out the area of round tables, rangoli designs, gardens and tanks.
Getting the diameter of a pipe or tree from a string measurement around it.
Sizing lids, wheels, bangles and rotis in everyday work.
Class 6 to 10 problems on circles.
How do I find the radius from the area?
Divide the area by π and take the square root. An area of 100 gives a radius of about 5.642.
How do I find the diameter from the circumference?
Divide the circumference by π. A circumference of 44 cm gives a diameter of about 14 cm.
Should I use 22/7 or 3.14 for π?
Both are approximations. 22/7 is handy when the radius is a multiple of 7. This calculator uses the full value of π, so its answers may differ slightly from textbook answers that use 22/7.
What is the difference between a chord and a diameter?
A chord joins any two points on the circle. A diameter is the longest chord, the one that passes through the centre.