Circle Calculator (Radius, Diameter, Circumference and Area)

Enter only one value you know out of radius, diameter, circumference and area. The other three are calculated together.

Radius R

Diameter D

Circumference C

Area A

Fill in only one field (two or more gives an error). Enter a number greater than 0. The units follow your input (if the radius is in inches, the circumference is in inches and the area in in²).

Result and figure

Enter any one of radius, diameter, circumference or area in the fields on the left and press "Calculate". The result will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formulas and figures
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter just one value you know out of radius, diameter, circumference and area, and you get the other three right away
It also works backward from the circumference or the area, such as "What is the radius of a circle with a circumference of 100 in?" or "What is the diameter of a circle with an area of 100 in²?"
Besides the decimal answer, it shows the exact answer in terms of \(\pi\) (for a radius of 5, circumference \(= 10\pi\) and area \(= 25\pi\))
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

The calculation uses \(\pi = 3.14159\ldots\) (the "3.14" used in school is a rounded value of it). You do not need to choose a unit. Enter the radius in inches and the diameter and circumference are in inches and the area in in² (for feet, ft and ft²).

What is this calculation used for?

Choosing a pizza or cake size (compare by area)

An 18-inch pizza has an area of \(\pi \times 9^2 \approx 254\) in², and a 12-inch pizza \(\pi \times 6^2 \approx 113\) in². The diameter is only 1.5 times larger, but the amount you can eat (the area) is \(1.5^2 = 2.25\) times larger.
So one 18-inch pizza has more pizza than two 12-inch pizzas (about 226 in²). To compare deals like this correctly, use the area formula, not the diameter.

Finding a tree's diameter from its girth (forestry and landscaping)

You cannot measure the diameter of a standing tree directly, so you wrap a tape measure around the trunk (the circumference) and convert it with \(D = C \div \pi\). A trunk 60 in around is about 19.1 in in diameter.
Foresters actually use a "diameter tape" (D-tape) with this calculation built into its markings (it treats the trunk's cross section as a circle, so the result is an approximation).

Planning materials for a round flower bed or garden (gardening and farming)

For a round flower bed with a radius of 5 ft, the area is \(\pi \times 5^2 \approx 78.5\) ft², and the distance around it is \(2\pi \times 5 \approx 31.4\) ft.
From the area you can estimate how much soil, fertilizer or sod you need, and from the circumference how much edging or brick to buy, before you go to the store.

Why are the starting lines on a running track staggered? (sports)

The two curves of a running track together make exactly one full circle, so running one lane farther out (lanes are about 1.22 m, or 48 in, wide) adds \(2\pi \times 1.22 \approx 7.7\) m per lap.
In the 400 m race, the outer lanes start farther ahead to cancel out this difference found with the circumference formula (the official rules also take into account where the measuring line is).

Cross-sectional area of pipes and hoses (plumbing and engineering)

A pipe with an inside diameter of 1 in has a cross-sectional area of \(\pi \times 0.5^2 \approx 0.785\) in². With a 2-inch inside diameter it is \(\pi \times 1^2 \approx 3.14\) in², 4 times as much.
"Double the diameter and the cross-sectional area becomes 4 times larger (because it is squared)" is a basic rule when choosing the size of water pipes, ducts and electrical wires.

How far a tire or wheel goes in one turn (bicycles and cars)

A bicycle tire with an outside diameter of 26 in moves forward one circumference per turn, \(\pi \times 26 \approx 81.7\) in (about 6.8 ft). In 100 turns it goes about 681 ft.
Bike computers and car speedometers find speed and distance from this "one turn = one circumference" rule and how fast the wheel turns.

Formulas and figures

Formula for the diameter

Figure

Standard notation (the usual math form)

\(D\) \(=\) \(2\) \(\times\) \(R\)

In words (symbols replaced with words)

③ \(D\): diameter \(=\) ② \(2\): two radii \(\times\) ① \(R\): radius

The formula in words

① Take the \(R\): radius

② multiply it by \(2\): two radii

③ and you get the \(D\): diameter

Quick example

The diameter of a circle with a radius of 5 in is

\(D\): diameter \(=\) \(2\) \(\times\) radius (5 in)

\(D = 2 \times 5 = 10\)

Key idea

The diameter is the length from edge to edge through the middle (the center) of the circle, exactly twice the radius. The other way around, if you know the diameter, divide it by 2 to get the radius (\(R = D \div 2\)).

Formula for the circumference

Figure

Standard notation (the usual math form)

\(C\) \(=\) \(2\) \(\times\) \(\pi\) \(\times\) \(R\)

In words (symbols replaced with words)

④ \(C\): circumference \(=\) ③ \(2\): two radii \(\times\) ② \(\pi\): pi \(\times\) ① \(R\): radius

The formula in words

① Take the \(R\): radius

② multiply it by \(\pi\): pi (about 3.14)

③ multiply by \(2\): two radii

④ and you get the \(C\): circumference

Quick example

The circumference of a circle with a radius of 5 in is

\(C\): circumference \(=\) \(2\) \(\times\) \(\pi\): pi \(\times\) radius (5 in)

\(C = 2 \times \pi \times 5 = 10\pi\)

\(10\pi = 10 \times 3.14159\ldots \approx 31.4\)

Key idea

"Radius × 2" is the diameter, so this formula is the same as "circumference = pi × diameter" (\(C = \pi D\)). The "circumference = diameter × 3.14" you learn in school is this formula with pi rounded to 3.14. Pi (\(\pi\)) is the number of times the circumference is longer than the diameter. It is \(3.14159265\ldots\), a decimal that goes on forever without repeating (an irrational number). For a circle of any size, this ratio is always the same.

Formula for the area

Figure

Standard notation (the usual math form)

\(A\) \(=\) \(\pi\) \(\times\) \(R\) \(2\)

In words (symbols replaced with words)

④ \(A\): area \(=\) ③ \(\pi\): pi \(\times\) ① \(R\): radius ② \(2\): exponent for squaring

The formula in words

① Take the \(R\): radius

② and square it (radius × radius)

③ multiply by \(\pi\): pi (about 3.14)

④ and you get the \(A\): area

Quick example

The area of a circle with a radius of 5 in is

\(A\): area \(=\) \(\pi\): pi \(\times\) radius (5 in) squared

\(A = \pi \times 5^2 = 25\pi\)

\(25\pi = 25 \times 3.14159\ldots \approx 78.5\)

Key idea

This is the same as "area = radius × radius × pi" from school. There are two common mistakes. (1) Squaring the diameter instead of the radius (always change it to the radius first, then square it). (2) Mixing up "squared" and "times 2" (5 squared is \(5 \times 5 = 25\), while 5 times 2 is \(5 \times 2 = 10\)).

Formula for the radius from the circumference

Figure

Standard notation (the usual math form)

\(R\) \(=\) \(C\) \(\div\) \(2\) \(\div\) \(\pi\)

In words (symbols replaced with words)

④ \(R\): radius \(=\) ① \(C\): circumference \(\div\) ② \(2\): two radii \(\div\) ③ \(\pi\): pi

The formula in words

① Take the \(C\): circumference

② divide it by \(2\): two radii

③ then divide by \(\pi\): pi (about 3.14)

④ and you get the \(R\): radius

Quick example

A tape measure around a tree trunk (the circumference) reads 100 in. The radius of the trunk is

\(R\): radius \(=\) circumference (100 in) \(\div\) \(2\) \(\div\) \(\pi\): pi

\(R = 100 \div 2 \div \pi = \dfrac{50}{\pi} \approx 15.9\)

Key idea

This is the circumference formula \(C = 2\pi R\) worked backward. It is the same as "circumference ÷ \(2\pi\)" (dividing by \(2\pi \approx 6.28\)). You can also find "circumference ÷ \(\pi\) = diameter" first and then divide by 2; the answer is the same.

Formula for the radius from the area

Figure

Standard notation (the usual math form)

\(R\) \(=\) \(\sqrt{A \div \pi}\)

In words (symbols replaced with words)

② \(R\): radius \(=\) ① square root of area \(A\) ÷ pi \(\pi\)

The formula in words

① Find the square root of area \(A\) divided by pi \(\pi\) (the positive number that gives \(A \div \pi\) when squared)

② and you get the \(R\): radius

Quick example

The radius of a circle with an area of 100 in² is

\(R\): radius \(=\) \(\sqrt{100 \div \pi}\)

\(R = \sqrt{100 \div \pi} \approx \sqrt{31.83} \approx 5.64\)

Key idea

This is the area formula \(A = \pi R^2\) worked backward. Dividing the area by \(\pi\) gives the radius squared, so taking its square root (\(\sqrt{\ }\), the positive number that gives that number when squared) takes you back to the radius. You can find a square root with the "√" key on a calculator or the SQRT function in Excel.

Circle calculations rest on three formulas - "diameter = 2 × radius", "circumference = pi × diameter" and "area = pi × radius × radius". If you know any one value, work the formula backward to get the radius, and then you can find all the rest. Pi (π) is 3.14159…, a number that goes on forever; 3.14 is often used when calculating by hand.

Symbols and terms

Symbols

\(R\)	ar	The radius - the length from the center of the circle to the edge. Many US textbooks write it as a lowercase \(r\).
\(D\)	dee	The diameter - the length from edge to edge through the center, twice the radius (\(D = 2R\)).
\(C\)	see	The circumference - the distance once around the circle.
\(A\)	a	The area - the size of the space inside the circle. If lengths are in inches, the area is in in².
\(\pi\)	pi	Pi - the number of times the circumference is longer than the diameter. It is \(3.14159265\ldots\) and goes on forever. In school it is often rounded to 3.14.
\(R^2\)	R squared	Radius × radius. The small 2 at the upper right is an exponent that tells you to multiply the number by itself. (Example - \(5^2 = 5 \times 5 = 25\))
\(\sqrt{\ }\)	square root	The positive number that gives the number inside when squared. (Example - \(\sqrt{25} = 5\), and 5 squared is 25 again)

Terms

circle	The shape made of all the points on a flat surface that are the same distance from one point (the center). That distance is the radius.
radius	The length from the center of a circle to its edge. It is the most basic value that sets the size of a circle, and every calculation on this page first converts to the radius.
diameter	The length of a line segment drawn through the center from one side of the circle to the other. It is exactly twice the radius.
circumference	The distance once around a circle. For any circle, "circumference ÷ diameter" is always pi (about 3.14).
pi	The number of times the circumference is longer than the diameter (symbol π). It is 3.14159265…, a decimal that goes on forever without repeating, and it has been proven that no fraction can express it exactly (an irrational number). People have looked for more accurate values ever since Archimedes in ancient Greece.
irrational number	A number that cannot be written exactly as a fraction (integer ÷ integer). Pi is the best-known example, which is why calculations either use a rounded value such as 3.14 or leave π as it is.
square root	A number that gives the original number when squared (symbol √). It is used to work back from the area to the radius. It is taught in middle school math (around Grade 8).

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.

Circles and pi (Grade 7)	Knowing the words radius, diameter and center, and that the diameter is twice the radius Being able to find the circumference as "circumference = diameter × pi (3.14)", and knowing that pi is how many times longer the circumference is than the diameter
Area of a circle (Grade 7)	Being able to find the area of a circle as "area = radius × radius × pi" Knowing the difference between a unit of length (in) and a unit of area (in²)
Writing expressions with variables (Grades 6–7)	Being able to write a formula with letters and no multiplication sign, as in \(C = 2\pi R\) Being able to leave pi as the letter \(\pi\) in a formula
Square roots (Grade 8)	Knowing that \(\sqrt{a}\) is "the positive number that gives \(a\) when squared" (used to work back from the area to the radius)
Multiplying and dividing decimals (Grades 5–6)	Being able to multiply by 3.14 or divide by 3.14 on paper

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to find the diameter

Radius R	5
Diameter D	=2*B1

Table to find the circumference

Radius R	5
Circumference C	=2PI()B1

Table to find the area

Radius R	5
Area A	=PI()*B1^2

Table to find the radius from the circumference

Circumference C	100
Radius R	=B1/(2*PI())

Table to find the radius from the area

Area A	100
Radius R	=SQRT(B1/PI())

After pasting, B1 is your input and B2 is calculated automatically.
"PI()" is a function that returns pi (3.14159…), "SQRT()" finds a square root, and "^2" squares a number.
In the second table, for example, B2 shows about 31.42 (the circumference of a circle with a radius of 5). The fourth table shows about 15.92 and the fifth about 5.64. Just replace B1 with your own number.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to find the diameter

Radius R	5
Diameter D	=2*B1

Table to find the circumference

Radius R	5
Circumference C	=2PI()B1

Table to find the area

Radius R	5
Area A	=PI()*B1^2

Table to find the radius from the circumference

Circumference C	100
Radius R	=B1/(2*PI())

Table to find the radius from the area

Area A	100
Radius R	=SQRT(B1/PI())

The same formulas as in Excel (PI() and SQRT()) work as is. Copy the whole table, paste it into cell A1, and replace B1 with your own number.

How to calculate it in Python

import math

radius = 5  # radius (enter the value you know)

diameter = radius * 2                 # diameter
circumference = 2 * math.pi * radius  # circumference
area = math.pi * radius ** 2          # area

print(f"Diameter: {diameter}")
print(f"Circumference: {circumference}")
print(f"Area: {area}")

# Working back: find the radius from the circumference or the area
radius_from_circumference = 100 / (2 * math.pi)  # radius of a circle with circumference 100
radius_from_area = math.sqrt(100 / math.pi)      # radius of a circle with area 100
print(f"Radius of a circle with circumference 100: {radius_from_circumference}")
print(f"Radius of a circle with area 100: {radius_from_area}")

Runs with the standard library only. "math.pi" is pi (3.14159…), "math.sqrt" is the square root and "**" is a power (squaring here). Change the radius at the top and run it.

How to write it in LaTeX and other math languages (copy and paste)

Formula for the diameter

D = 2R

D = 2R

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>D</mi>
    <mo>=</mo>
    <mn>2</mn>
    <mi>R</mi>
  </mrow>
</math>

D = 2R

2 r

d := 2*r;  # D (the differential operator) is reserved in Maple, so all variables are lowercase

D = 2*R;

D = 2R

Formula for the circumference

C = 2πR

C = 2\pi R

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>C</mi>
    <mo>=</mo>
    <mn>2</mn>
    <mi>&#x03C0;</mi>
    <mi>R</mi>
  </mrow>
</math>

C = 2 pi R

2 Pi r

C := 2*Pi*R;

C = 2*pi*R;

C = 2πR

Formula for the area

A = πR²

A = \pi R^{2}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>A</mi>
    <mo>=</mo>
    <mi>&#x03C0;</mi>
    <msup><mi>R</mi><mn>2</mn></msup>
  </mrow>
</math>

A = pi R^2

Pi r^2

A := Pi*R^2;

A = pi*R^2;

A = πR^2

Formula for the radius from the circumference

R = C ÷ (2π)

R = \dfrac{C}{2\pi}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <mfrac>
      <mi>C</mi>
      <mrow><mn>2</mn><mi>&#x03C0;</mi></mrow>
    </mfrac>
  </mrow>
</math>

R = C/(2 pi)

c/(2 Pi)

R := C/(2*Pi);

R = C/(2*pi);

R = C/(2π)

Formula for the radius from the area

R = √(A ÷ π)

R = \sqrt{\dfrac{A}{\pi}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <mi>R</mi>
    <mo>=</mo>
    <msqrt>
      <mfrac><mi>A</mi><mi>&#x03C0;</mi></mfrac>
    </msqrt>
  </mrow>
</math>

R = sqrt(A/pi)

Sqrt[a/Pi]

R := sqrt(A/Pi);

R = sqrt(A/pi);

R = √(A/π)

How to have ChatGPT do the calculation

You are a calculation assistant for circles. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

1. Find the diameter, circumference and area of a circle with a radius of 5 in.
2. Find the radius of a circle with a circumference of 100 in.
3. Find the radius of a circle with an area of 100 in².

Use math.pi for pi. Show the formulas you used and the numbers from the execution result (to 2 decimal places).

How to Use

1

Enter your numbers

Type the numbers you want to calculate with into the input fields
2

Calculate

Press the "Calculate" button
3

Check the result

The result appears on the spot. The same page also explains the idea behind the calculation and the formula