Last updated: July 16, 2026
Area of a Circle Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Area of a Circle Calculator converts radius, diameter, or circumference into all four core circle outputs: radius, diameter, circumference, and area. It uses the standard geometry relationships d = 2r, C = 2πr, and A = πr², while also supporting equivalent forms such as A = πd²/4 and A = C²/(4π).
To find the area of a circle, use A equals pi times radius squared. If you know the diameter, divide it by two to get the radius. If you know the circumference, divide it by two pi to get the radius first.
Key Takeaways
- The core formula is A = πr².
- If you know diameter, convert it to radius with r = d/2 before finding area.
- If you know circumference, convert it with r = C/(2π) or use A = C²/(4π).
- Diameter, radius, and circumference use linear units, but area uses square units.
- Doubling the radius makes the area four times larger.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
A = π × r²
Where:
- A=Area of the circle(square units)
- r=Radius of the circle(units)
- C=Circumference of the circle(units)
Worked Examples
Find area from radius
A circle has radius 5 cm and you want its area and related measures.
- 1Start with r = 5 cm.
- 2Diameter = 2r = 10 cm.
- 3Circumference = 2πr = 2π × 5 ≈ 31.42 cm.
- 4Area = πr² = π × 5² = 25π ≈ 78.54 cm².
Find area from diameter
A circular tabletop has diameter 12 cm and you need its surface area.
- 1Start with d = 12 cm.
- 2Radius = d/2 = 6 cm.
- 3Circumference = πd = 12π ≈ 37.70 cm.
- 4Area = π(d/2)² = π × 6² = 36π ≈ 113.10 cm².
Find area from circumference
You know the circumference is 31.42 cm and want the enclosed area.
- 1Start with C = 31.42 cm.
- 2Radius = C/(2π) = 31.42/(2π) ≈ 5.00 cm.
- 3Diameter = C/π ≈ 10.00 cm.
- 4Area = πr² = π × 5² ≈ 78.54 cm².
Introduction
The Area of a Circle Calculator helps you move between the three most common circle measurements: radius, diameter, and circumference. Enter whichever value you know, and the calculator returns all four core results: radius, diameter, circumference, and area. If you also need the boundary length, try the circle perimeter calculator. For rectangular comparisons, our area rectangle calculator is useful too.
The main area formula
The standard formula for the area of a circle is A = πr². It says the enclosed space grows with the square of the radius, so doubling the radius makes the area four times larger. This relationship is discussed clearly by Wolfram MathWorld and Encyclopaedia Britannica.
How to calculate from radius
When the radius is known, the calculation is most direct: set r = radius, then compute d = 2r, C = 2πr, and A = πr². This is usually the easiest input method because the radius appears directly in the area formula. If you want a broader comparison with other curved shapes, see our ellipse area calculator.
How to calculate from diameter
If the diameter is the only value you know, first convert it to radius with r = d/2. Then the area becomes A = π(d/2)², which is equivalent to A = πd²/4. This method is common in manufacturing and construction drawings where full width is listed instead of radius. For another simple geometry conversion, compare with the area of a square calculator.
How to calculate from circumference
When only the distance around the circle is known, use r = C/(2π) and d = C/π. Substituting that radius into the area formula gives A = π(C/(2π))², which simplifies to A = C²/(4π). Khan Academy also explains why circumference and radius are linked through π at Khan Academy.
Units and scaling
Radius, diameter, and circumference use linear units such as cm, m, or ft, while area uses square units such as cm², m², or ft². Because area depends on a squared value, a small change in radius can create a much larger change in area. This is why a circle with radius 10 has four times the area of a circle with radius 5, not twice the area.
Real-world uses of circle area
Circle area is used when estimating paint for a round surface, planning a circular garden bed, sizing a round rug, or computing cross-sectional areas in engineering. If the shape is only half or part of a circle, related tools like the area of a sphere calculator and area right triangle calculator can help you compare how geometry changes between curved and straight-edged figures.
Quick Reference Card
Area of a Circle Quick Reference
Quick reference • Area of a Circle Calculator
A = πr²Valid range: Use positive values only for radius, diameter, and circumference.
Common Values
⚠ Watch Out
- •Do not mix units unless you convert them first.
- •Area must be reported in square units, not plain units.
- •Negative or zero circle measurements are not physically valid.
- •Rounding π too aggressively can noticeably change the final area.
Pro Tips
- →Use radius directly whenever possible because it gives the simplest formula.
- →If only diameter is given, halve it before squaring.
- →If only circumference is given, use A = C²/(4π) for a direct shortcut.
- →Check whether your problem asks for exact form in terms of π or a decimal approximation.
FAQs
What is the formula for the area of a circle?
The main formula is A = πr², where r is the radius. If you know the diameter, you can also use A = π(d/2)². If you know the circumference, you can use A = C²/(4π).
How do I find the area from diameter?
Divide the diameter by 2 to get the radius, then apply A = πr². Equivalently, use A = πd²/4.
How do I find the area from circumference?
First calculate the radius using r = C/(2π). Then substitute that radius into A = πr². The shortcut form is A = C²/(4π).
Why is the area measured in square units?
Area describes two-dimensional surface coverage, so it is always expressed in square units such as cm², m², or ft² rather than plain linear units.
What is the relationship between radius and diameter?
The diameter is always twice the radius, so d = 2r. The radius is half the diameter, so r = d/2.
What happens to area when the radius doubles?
The area becomes four times larger because the radius is squared in the formula A = πr².