Circle Area Calculator — enter radius, diameter, or circumference and get instant area with π.
Fast conversions to in², ft², cm², and m².
Circle Area Calculator – compute area from radius, diameter, or circumference.
Circle Area Calculator – Find Area, Radius & Diameter Instantly
Our circle area calculator lets you compute the area of a circle from any single input —
radius (r), diameter (d), or circumference (C). The tool also reveals the missing values
(r, d, C) automatically and shows full unit outputs in
in², ft², cm², and m².
Built on the standard formulas with π (π ≈ 3.1416), it’s perfect for quick geometry, classwork, and real-world measurements.
Enter one value to see all results instantly.
Keywords: area of a circle calculator, radius & diameter, π value 3.1416.
Which Input Should I Use? (r vs d vs C)
Many users wonder whether to enter the radius (r), diameter (d), or circumference (C) when using the Circle Area Calculator.
Here’s how to decide which input works best for your measurement:
- Radius (r): Use this when you can measure from the center to the edge. It’s the simplest and most direct method.
Formula: A = π × r². - Diameter (d): If you only know the full width of the circle, use this option.
Formula: A = (π × d²) / 4.
Tip: r = d ÷ 2. - Circumference (C): Ideal when you can wrap a tape measure around the outer edge.
Formula: A = C² ÷ (4π).
💡 Practical Tip: For large objects like round tables or pipes, measure the circumference with a flexible tape.
For smaller circles (like lids or coins), use a ruler to get the diameter. If the edge has thickness, measure the inner diameter for accurate area.
Keywords: how to calculate the area of a circle, area using diameter, circumference to area.
Circle Area Formula
The area of a circle depends entirely on its size — whether you know the radius (r), diameter (d), or circumference (C).
Each gives you a direct path to calculate the same result using π (pi ≈ 3.1416).
- From Radius (r): A = π × r²
- From Diameter (d): A = (π × d²) / 4
- From Circumference (C): A = C² / (4π)
These three versions of the circle area formula are mathematically equivalent — they only change depending on which value you start with.
Our calculator automatically switches between them when you input radius, diameter, or circumference.
💡 Tip for precision: Use π = 3.1416 for quick manual calculations, or keep π as a symbol for exact results when working with algebraic expressions.
Keywords: area of circle formula, formula for a circle, π formula.
Example Calculations
Here are some quick examples that show how the circle area formula works using radius, diameter, and circumference.
You can try the same values directly in the calculator above to verify the results.
1️⃣ Using Radius
r = 9 in → A = π × 9² = 254.47 in²
✅ This answers: “What is the area of a 9 inch circle?”
2️⃣ Using Diameter
d = 20 in → A = (π × 20²) / 4 = 314.16 in²
✅ This answers: “What is the area of a 20 inch circle?”
3️⃣ Using Circumference
Suppose C = 37.70 in → A = C² / (4π) = 113.10 in²
This is consistent with the calculator’s result for a circle with about r = 6 in.
💡 Try it yourself: Enter these values above and instantly switch between radius, diameter, and circumference
to see how all three formulas give the same area result.
Keywords: area of a 9 inch circle, area of a 20 inch circle, calculate circle area.
Quick Conversion Table
The Circle Area Calculator automatically converts between square inches (in²),
square feet (ft²), and square centimeters (cm²).
Here’s a quick reference for common unit conversions:
| Square Inches (in²) | Square Feet (ft²) | Square Centimeters (cm²) |
|---|---|---|
| 1 in² | 0.00694 ft² | 6.4516 cm² |
| 50 in² | 0.347 ft² | 322.58 cm² |
| 100 in² | 0.694 ft² | 645.16 cm² |
| 500 in² | 3.47 ft² | 3225.8 cm² |
| 1000 in² | 6.94 ft² | 6451.6 cm² |
💡 Note: 1 ft² = 144 in².
You can use these quick conversions for flooring, circular pools, or garden measurements.
Keywords: area converter, square inches to square feet, area in cm²/ft².
Measuring Tips & Common Mistakes
Getting accurate results in the Circle Area Calculator starts with proper measurements.
Whether you’re working with a small ring, a plate, or a large circular pool — here’s how to measure correctly and avoid common errors.
- Measure the inner diameter if your circle has a rim or border — outer edges can distort the area value.
- Don’t confuse radius (r) with diameter (d): remember, d = 2r.
- Don’t round π too early: use the full value (3.1416) until the final step or let the calculator handle precision automatically.
- For large circles, measure circumference (C) instead of a single diameter — it’s often easier and more accurate for big objects like tanks or fields.
💡 Pro tip: Always use consistent units (e.g., all in inches or all in centimeters) to prevent conversion errors when calculating circle area.
Keywords: how to calculate circle area, measurement tips.
FAQs – Circle Area Explained
1. How to calculate circle area?
The area of a circle is found using the formula A = π × r², where r is the radius.
Just square the radius and multiply by π (≈ 3.1416).
Example: radius = 5 in → A = 3.1416 × 5² = 78.54 in².
2. What is 2πr of a circle?
2πr represents the circumference of a circle — the total distance around it.
It’s not the area, but it’s related: if you know the circumference (C), area can be found with A = C² / (4π).
3. Is 3.14 the area of a circle?
No — 3.14 is just a rounded value of π (pi), a constant used to calculate the area.
The area changes depending on the radius, but π (≈ 3.1416) stays the same in every formula.
4. What is the area of a 9 inch circle?
Using A = π × r² → r = 9 in → A = 3.1416 × 9² = 254.47 in².
5. What is the area of a 20 inch circle?
Using diameter = 20 in → r = 10 in → A = 3.1416 × 10² = 314.16 in².
6. What is a formula for a circle?
The main formula is A = πr² for area, and C = 2πr for circumference.
Both use the same constant π, where π ≈ 3.1416.
7. How do you calculate area with diameter?
Divide the diameter by 2 to get the radius, then apply A = πr², or use the shortcut formula
A = (π × d²) / 4 to find the area directly from diameter.
💡 Tip: The Circle Area Calculator on this page handles all these formulas for you — just enter one known value (radius, diameter, or circumference) and it does the rest instantly.
Keywords: circle area calculator, area of a circle calculator, how to calculate circle area, π formula.
Related Tools – More Geometry & Area Calculators
Explore more free geometry tools that complement the Circle Area Calculator.
Each helps you calculate different shapes — from rectangles and triangles to circular sectors and ellipses.
- Sector Area Calculator – find the area of circle sectors using angle and radius.
- Ellipse Area Calculator – for oval or elliptical shapes.
- Triangle Area Calculator – works for base–height or three sides (Heron’s formula).
- Rectangle Area Calculator – calculate area and perimeter instantly.
- Circumference Calculator – coming soon for fast circle perimeter results.
💡 Tip: Use these related tools to explore more shape formulas and compare different area calculations — all free on PixelsCalculator.
References
Source reference included for educational transparency and verification of geometric formulas.