Circle calculator: radius, diameter, circumference, area

• From the radius: $r = 5$ cm. $d = 10$ cm, $C = 2\pi \times 5 = 10\pi \approx 31.42$ cm, $A = \pi \times 25 = 25\pi \approx 78.54$ cm².
• From the area: $A = 50$ cm². $r = \sqrt{50 \div \pi} \approx 3.99$ cm.
• From the circumference: $C = 31.4$ cm. $r = 31.4 \div 2\pi \approx 5.00$ cm.

To find the radius from the area, divide by $\pi$ then take the square root: $r = \sqrt{A \div \pi}$. From the circumference, divide by $2\pi$: $r = C \div 2\pi$. These reverse steps are common in exam questions ("a circle has an area of 50 cm², find its circumference"), and the calculator shows both stages.

$\pi$ (pi) is the ratio of any circle's circumference to its diameter: about 3.14159. It never ends or repeats. Use the $\pi$ button on your calculator rather than 3.14 for accuracy, unless the question tells you to use 3.14 or 22/7.

A chord is a straight line across the circle (the diameter is the longest chord). A tangent touches the circle at one point, at right angles to the radius. An arc is part of the circumference, and a sector is a "pizza slice" between two radii: our arc length and sector area calculator handles those.

• Using the diameter in $\pi r^2$.
• Mixing up the formulas: circumference is a length ($2\pi r$), area is in square units ($\pi r^2$).
• Squaring after multiplying by $\pi$ instead of squaring the radius first.

Practise with our circles questions.

• On non-calculator papers, give answers in terms of $\pi$, such as $25\pi$ cm².
• For semicircles, halve the area, and for the perimeter add the diameter to half the circumference.
• Round to 3 significant figures unless told otherwise, and include units.

• Wheels: one full turn of a wheel moves it forward by its circumference. A bike wheel with a diameter of 0.7 m travels $\pi \times 0.7 \approx 2.2$ m per turn, so about 455 turns per kilometre.
• Pizza: a 12-inch pizza (radius 6) has an area of $36\pi \approx 113$ square inches, but a 16-inch one has $64\pi \approx 201$: nearly twice as much for a third more width.
• Running tracks: the curved ends are semicircles, so lanes further out are longer, which is why races start staggered.