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π = pi = 3.1415926535898
√ = square root
Calculator Use
Use this circle calculator to find the area, circumference, radius or diameter of a circle. Given any one variable A, C, r or d of a circle you can calculate the other three unknowns.
Units: Note that units of length are shown for convenience. They do not affect the calculations. The units are in place to give an indication of the order of the results such as ft, ft2 or ft3. Any other base unit can be substituted.
Circle Formulas in terms of Pi π, radius r, and diameter d
r = d/2
d = 2rA = πr2 = πd2/4
C = 2πr = πd
Circle Calculations:
Using the formulas above and additional formulas you can calculate properties of a given circle for any given variable.
Calculate A, C and d | Given r Given the radius of a circle calculate the area, circumference and diameter. Putting A, C and d in terms of r the equations are:
\[A = \pi r^2 \]
\[C = 2 \pi r \]
\[d = 2r \]
Calculate r, C and d | Given A Given the area of a circle calculate the radius, circumference and diameter. Putting r, C and d in terms of A the equations are:
\[r = \sqrt{\frac{A}{\pi}} \]
\[C = 2 \pi r = 2 \pi \sqrt{\frac{A}{\pi}} \]
\[ d = 2r = 2 \sqrt{\frac{A}{\pi}} \]
Calculate A, r and d | Given C Given the circumference of a circle calculate the radius, area and diameter. Putting A, r and d in terms of C the equations are:
\[r = \frac{C}{2 \pi} \]
\[A = \pi r^2 = \pi \left(\frac{C}{2 \pi}\right)^2 = \frac{\pi C^2}{4 \pi^2} = \frac{C^2}{4 \pi} \]
\[d = 2r = \frac{2C}{2 \pi} = \frac{C}{\pi} \]
Calculate A, C and r | Given d Given the diameter of a circle calculate the radius, area and circumference. Putting A, C and r in terms of d the equations are:
\[r = \frac{d}{2} \]
\[A = \pi r^2 = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} \]
\[C = 2 \pi r = 2 \pi \frac{d}{2} = \pi d \]
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How to Calculate Circumference, Diameter, Area, and Radius
The circle calculator finds the area, radius, diameter and circumference of a circle labeled as a, r, d and c respectively.
For those having difficulty using formulas manually to find the area, circumference, radius and diameter of a circle, this circle calculator is just for you. The equations will be given below so you can see how the calculator obtains the values, but all you have to do is input the basic information. The calculator does the rest.
Finding the Circumference:
The circumference is similar to the perimeter in that it is the total length needed to draw the circle.
We note the circumference as c.
c = 2πr
or
c = πd
This depends on whether or not you know the radius (r) or the diameter (d)
Let’s calculate one manually, for example.
If r = 6 cm, the the circumference is c = 2π(6) = 12π cm, if writing in terms of π. If you prefer a numerical value, the answer rounded to the nearest tenth is 37.7 cm.
Suppose you only know the diameter? If the diameter is 8 cm, then the circumference is c = π(8) = 8π or 25.1 cm, rounded to the nearest tenth.
A great thing about the formulas is that you can manipulate it to solve for an unknown if you know one of the other quantities. For example, if we know the circumference, but don’t know the radius, you can solve c = 2πr for r and get \(r = \frac{c}{2\pi}\). Similiarly, if you want the diameter from the circumference, simply take c =πd and solve for d to get d = \(\frac{c}{\pi}\).
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Finding the Area:
Let a = area of the circle
a = πr²
If you know the diameter and not the radius, simply divide the diameter by 2 to get the radius and still use the formula above.
Again, the formula can be used to solve for the radius, if you know the area. Simply divide a by π to get r² and take the square root of
the result.
If you wish to know the diameter from the area, follow the procedure above but double the result you get for r. This is because the diameter is twice the length of the radius.
Try an example manually to get the area.
Suppose r = 5 inches
a = πr²
a = π(25) = 25π
If rounding to the nearest tenth the area is 78.5 square inches.
If you know the diameter, simply divide by 2 to get the radius and use the same formula as above.
Of course, you don’t have to go through all the manual calculations to use this calculator. Simply input the information you know and the rest will be computed for you nearly instantly.
The area of a circle calculator helps you compute the surface of a circle given a diameter or radius. Our tool works both ways - no matter if you're looking for an area to radius calculator or a radius to the area one, you've found the right place ◔
We'll give you a tour of the most essential pieces of information regarding the area of a circle, its diameter, and its radius. We'll learn how to find the area of a circle, talk about the area of a circle formula, and discuss the other branches of mathematics that use the very same equation.
So, let's see how to find the area of a circle. There are several ways to achieve it. Here, we can calculate the area of a circle using a diameter or using a radius.
| 💡 The diameter is the line that crosses the center of the figure and touches both of its margins. The radius begins at the center of the figure and ends at the figure's margin. |
You can find the diameter of a circle by multiplying the radius of a circle by two:
Diameter = 2 * Radius
Area of a circle radius. The radius of a circle calculator uses the following area of a circle formula:
Area of a circle = π * r2
Area of a circle diameter. The diameter of a circle calculator uses the following equation:
Area of a circle = π * (d/2)2
Where:
- π is approximately equal to 3.14. It doesn't matter whether you want to find the area of a circle using diameter or radius - you'll need to use this constant in almost every case.
🔎 Another relevant aspect of circles is their circumference. You can learn more about it and its relationship with area in our circle formula calculator
Now that you know how to calculate the area of a circle, we encourage you to try our other circle calculators:
A sector of a circle is section of a circle between two radii. You can think of it as a giant slice of pizza.
It's a "cut-off" part of a circle, limited by a chord or a secant.
It's an angle with the vertex in the center, whose arms extend to the circumference.
You can easily calculate everything, the area of a circle, its diameter, and its radius, using our area of a circle calculator in a blink of an eye:
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Determine whether your given value is a diameter or a radius using the picture on the right and definitions available in the section above (you can calculate the area of a circle using its diameter as well as radius).
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Enter your value into the proper field of the calculator.
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It didn't take long - your results are here! We decided to include the step-by-step solution and all the most important data right below the calculator.
That is how to calculate the area of a circle in no time 😉.
The circle's area found with both the radius and diameter calculators serves as a base for many other equations - not only in mathematics but also in everyday life! Here are a few examples where knowing how to find the area of a circle might be useful:
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We need to know the surface area of a circle in order to calculate a cone's volume and its surface area 🎉
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Your pizza party wouldn't be complete without our pizza tool based on the diameter to area calculator 🍕
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We use calculations similar to this one when obtaining information about a sphere, such as sphere volume.🌐
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Do you fancy nice dresses? Maybe you love to sew? Discover our circle skirt calculator! Efficient sewing has never been easier. 👗