Circle Calculator
A circle with a radius of 5 has an area of about 78.54 and a circumference of about 31.42. This circle calculator finds the area, circumference, and diameter of any circle from a single measurement. Enter the radius (the distance from the center to the edge) or the diameter (the distance straight across through the center), and the tool fills in the other two values instantly using the standard circle formulas. Circle math shows up constantly outside the classroom: sizing a round rug or table for a room, figuring out how much edging wraps around a circular garden bed, cutting a circular piece of plywood or fabric to a target area, or checking a pipe's cross-sectional area for a plumbing or HVAC job. This tool handles the arithmetic so you can move straight from a single tape-measure reading to the area you need to cover or the length you need to wrap around the edge.
Quick answer
Area is calculated as pi times the radius squared, which measures the flat space enclosed inside the circle.
What this tells you
- •Area is calculated as pi times the radius squared, which measures the flat space enclosed inside the circle.
- •Circumference is calculated as 2 times pi times the radius, or equivalently pi times the diameter, which measures the distance around the outer edge.
- •Diameter is twice the radius, the straight-line distance across the circle through its center point.
- •Enter only the radius or the diameter, never both. The calculator derives whichever value you leave out.
- •Pi is an irrational constant, roughly 3.14159265358979. The calculator uses full floating-point precision internally and only rounds the numbers it displays.
- •Area grows with the square of the radius, so doubling the radius quadruples the area even though it only doubles the circumference.
- •All results, including radius, diameter, area, and circumference, are rounded to 4 decimal places for consistency.
How to Use
- 1Choose whether you are entering the radius or the diameter using the Input type selector.
- 2Enter the value in the box. Decimals such as 4.5 or 12.75 are accepted for real-world measurements like a tape-measure reading.
- 3Click Calculate to get the area, circumference, and diameter together, along with the formula used to reach the primary result.
- 4Match the result to your task. Use area for material coverage such as sod, fabric, or paint, and use circumference for edging, trim, or wrap-around lengths such as fencing or rope.
- 5Enter a new value anytime to recalculate. There is no need to reload the page or clear the previous result first.
How It Works
Formula
Area = pi x r squared. Circumference = 2 x pi x r. Diameter = 2 x r.The radius (r) is the distance from the center point to any point on the edge of the circle, and the diameter is twice that distance, measured straight across through the center. Area describes how much flat surface the circle covers, and it uses pi times the radius squared because area scales in two dimensions. Circumference describes the distance around the outer edge, and it uses 2 times pi times the radius because that distance scales in only one dimension. For example, a circle with a radius of 6 has an area of pi x 6 x 6 = 3.14159 x 36 = 113.10, and a circumference of 2 x 3.14159 x 6 = 37.70. If you only know the diameter, divide it by 2 first to get the radius before using either formula, or use circumference = pi x diameter directly, since that shortcut skips the radius step entirely.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Area of a small circle with radius 5 inches
Area = pi x 5 x 5 = 3.14159 x 25 = 78.54 square inches. Circumference = 2 x pi x 5 = 31.42 inches. Diameter = 2 x 5 = 10 inches. This is the arithmetic you would do to check how much glass or acrylic a round clock face needs to cover.
Circumference of a flower bed from a 10-foot diameter
A 10-foot diameter flower bed has a radius of 5 feet, so the area and circumference match the radius-5 example above. Circumference tells you how much edging material, like paver stones or a steel edging strip, wraps around the bed's perimeter.
Area of a round trampoline mat with a 7-foot radius
Area = pi x 7 x 7 = 3.14159 x 49 = 153.94 square feet, which is roughly the amount of safety padding needed to cover a 14-foot trampoline. Circumference = 2 x pi x 7 = 43.98 feet, useful for sizing a surrounding safety net or enclosure.
Dough area for a 12-inch diameter pizza
A 12-inch diameter means a 6-inch radius. Area = pi x 6 x 6 = 113.10 square inches of dough, and circumference = 2 x pi x 6 = 37.70 inches, which is the length of crust around the edge.
Tablecloth coverage for a patio table with a 4.5-foot radius
Area = pi x 4.5 x 4.5 = 3.14159 x 20.25 = 63.62 square feet of tabletop surface. Diameter = 9 feet, which is the flat measurement needed when shopping for a round tablecloth or a glass tabletop protector sized to the table.
Pool cover material for a 15-foot diameter above-ground pool
A 15-foot diameter pool has a 7.5-foot radius. Area = pi x 7.5 x 7.5 = 176.71 square feet, which approximates the vinyl or solar cover material needed. Circumference = 2 x pi x 7.5 = 47.12 feet, close to the length of a winter cover cable that wraps around the pool's edge.
Circle Area and Circumference by Radius
Common radius values and their corresponding diameter, area, and circumference.
| Radius | Diameter | Area | Circumference |
|---|---|---|---|
| 1 | 2 | 3.14 | 6.28 |
| 2 | 4 | 12.57 | 12.57 |
| 3 | 6 | 28.27 | 18.85 |
| 4 | 8 | 50.27 | 25.13 |
| 5 | 10 | 78.54 | 31.42 |
| 6 | 12 | 113.10 | 37.70 |
| 7 | 14 | 153.94 | 43.98 |
| 8 | 16 | 201.06 | 50.27 |
| 10 | 20 | 314.16 | 62.83 |
At a radius of exactly 2, area and circumference come out numerically equal (both 4 x pi), which is a coincidence of that specific radius, not a general rule.
Radius or diameter: picking the right input
Most tape measures make it easier to find a diameter than a radius. Laying a tape straight across the widest point of a circular object, like a table, pipe, or garden bed, gives you the diameter directly. Finding the radius by eye means guessing where the exact center sits, which is harder to do accurately without a compass or a string pinned at the middle.
If you already have a manufacturer spec, blueprint, or drawing, check which value it lists. Pipe and tubing specs are usually given as an inside or outside diameter, while some engineering drawings label the radius directly, often with an R prefix like R6 for a 6-unit radius. Enter whichever value you have and let the calculator handle the conversion instead of doing it by hand.
Either input path leads to the same area and circumference for a given circle, so there is no calculation advantage to converting by hand first. The main reason to convert manually is to double check a result or explain the math step by step, in which case dividing a diameter by 2 or doubling a radius is the full conversion needed.
Common mistakes
- Using the diameter instead of the radius in the area formula. Area uses pi times radius squared, not diameter squared. If you have the diameter, divide it by 2 first.
- Forgetting to square the radius. The area formula is pi times r times r, not pi times r.
- Confusing circumference with area. Circumference is the distance around the circle (2 times pi times r), while area is the space inside it (pi times r squared).
- Mixing units mid-calculation, such as measuring the radius in inches but expecting the area in square feet. Convert to a single unit before entering the value.
- Rounding pi too early. Rounding pi to 3.14 partway through a multi-step calculation can shift the final answer on larger circles, so round only the final displayed result.
- Assuming doubling the radius doubles the area. Area scales with the square of the radius, so doubling the radius quadruples the area, while circumference only doubles.
Embed this calculator on your site
Drop this single line where you want the calculator to appear. It is responsive, mobile-friendly, resizes automatically, and is free to use with attribution.
<script src="https://calctide.com/embed.js" data-tool="circle-calculator" async></script>Preview the embed at /embed/circle-calculator/.