Circle Radius Diameter Circumference Calculator
Find a circle radius, circle diameter, or circle circumference - all in one great little calculator
Works with all units of measure - and you can convert between them by clicking the different options.
Circle Equations and Circle Formula
To work out the radius of a circle, you need to measure the distance from the center of the circle to any point on the circumference. If you do not have a physical circle to measure, you can use the formula for the radius of a circle, which is:
r = C / (2 * π)
r = radius of the circle C = circumference of the circle π = Pi, which is approximately equal to 3.14159
To use this formula, you need to know the circumference of the circle. If you do not have the circumference, you can calculate it using the formula:
C = 2 * π * r
C = circumference of the circle r= radius of the circle π = Pi, which is approximately equal to 3.14159
To work out the radius of a circle, follow these steps:
If you have a physical circle, measure the distance from the center of the circle to any point on the circumference. This distance is the radius.
If you do not have a physical circle, measure the circumference of the circle.
Use the formula r = C / (2 * π) to calculate the radius, where C is the circumference you measured in step 2.
Alternatively, you can use the formula C = 2 * π * r to calculate the circumference if you already know the radius of the circle. Then, rearrange the formula to solve for r:
r = C / (2 * π)
These steps should allow you to easily work out the radius of a circle, whether you have a physical circle to measure or not. However... You could just use our fantastic Circle Tool - to work out either the radius, diameter or circumference, but at least now you know how to do it using formula!
Test Your Knowledge!
Question: The circumference of a circular pizza is 24 inches. What is the radius of the pizza in inches?
(Assume that the pizza is a perfect circle.)
- We know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
- We're given that the circumference of the pizza is 24 inches, so we can use that value into the formula:
24 = 2πr
- To solve for r, we can divide both sides by 2π: 24 / (2π) = r
- Using a calculator, we can simplify the expression to get: r ≈ 3.82 inches
- Therefore, the radius of the circular pizza is approximately 3.82 inches.
Circle History Lesson!
The concept of the radius of a circle has been known for thousands of years, and it was studied by ancient mathematicians in various parts of the world.
In ancient Egypt, the Rhind Mathematical Papyrus, which dates back to around 1650 BCE, includes several problems that involve the calculation of the radius of a circle. The papyrus shows that the Egyptians knew how to find the area of a circle by squaring its radius and multiplying it by Pi (which they approximated as 256/81, or approximately 3.16).
Similarly, ancient Greek mathematicians, such as Archimedes, Euclid, and Pythagoras, studied the properties of circles and developed various formulas related to their radii, circumferences, and areas. Archimedes, in particular, is known for his method of approximating Pi by inscribing and circumscribing polygons around a circle and calculating their perimeters.
Over time, the concept of the radius of a circle has become an important tool in various fields, including geometry, trigonometry, physics, and engineering. Today, the radius of a circle is used in many practical applications, from designing wheels and gears to calculating the trajectories of planets and satellites.
How to Use our Circle Tool
Our circle tool is very simple to use!
Just enter either the radius, diameter or circumference, and our calculator will do the rest - no need to click enter, it just updates automatically to show the correct answer. You can also change the unit of measure at the bottom
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