Geometry
Area of a Circle Calculator
Area of a circle from radius, diameter, or area; also diameter and circumference.
Free to use — no sign-up or login.
r = radius · d = diameter · C = circumference · A = area
Radius
Diameter
Area
Circumference
Amortization schedule
| # | Date | Payment | Principal | Extra | Interest | Balance |
|---|---|---|---|---|---|---|
This free area of a circle calculator reports the shaded disk and the boundary length from one measurement. Enter radius r = 3 (the default) and you get area A = 9π ≈ 28.27, circumference C = 6π ≈ 18.85, and diameter d = 6. Area is the interior of the circle; circumference is the length of the rim, not another name for the same number.
No account is required. Given can be radius, diameter, or area: if you already have the disk area, the same identities recover r and d, then circumference. How it works beside the form keeps A = πr², C = 2πr, d = 2r, and r = √(A/π) on separate lines.
Area of a circle formula
The area of a circle is the shaded disk enclosed by the rim: A = πr². Square the radius first, then multiply by π. With the default r = 3, r² = 9 and A = 9π ≈ 28.27 square units — centimeters of radius give square centimeters of area. That number is not the circumference; it is the surface of the disk.
Circumference formula — not the same as area
Circumference is the length of the rim: C = 2πr, or equivalently C = πd. At r = 3 that is C = 6π ≈ 18.85 length units, not 28.27. Area uses squared units (cm²); circumference uses length (cm). Do not paste one result into a field that expects the other. When the two numbers look interchangeable, check the FAQ on units.
Area from diameter
If you measured the full width instead of the center-to-rim distance, convert first: r = d/2, so A = π(d/2)² = πd²/4. The default diameter d = 6 is the same circle as r = 3, and the area is again 9π ≈ 28.27. Switching Given to Diameter shows that field; the outputs still list radius, diameter, area, and circumference.
Radius and diameter from area
The area identity rearranges to r = √(A/π) and d = 2√(A/π). Circumference from area is C = 2√(πA). The default area 9π ≈ 28.274333882308138 inverts to r = 3 and d = 6, the same circle you get from the radius default. Area must be positive; a zero or negative disk is not a circle this page will invert.
How to use this calculator
Choose Given: radius (default 3), diameter (default 6), or area (default 9π). Type the one quantity you have. The form always reports radius, diameter, area, and circumference so each formula stays labeled — the value you typed is echoed in the matching output. The How to Calculate Circle Area and Circumference tutorial keeps a radius-only playground for πr² and 2πr.
Related circle formulas
A half-disk is the Semicircle Area Calculator — half of πr², with the diameter added into the perimeter. The same r appears in the Sphere Calculator and the Cone Calculator. An ellipse with semi-axes a and b is the Ellipse Area Calculator. Expanding (x − h)² + (y − k)² = r² is the Equation of a Circle Calculator. For a rectangle, use Area.
Worked example: radius 3 and inverse from 9π
Radius r = 3. Diameter is twice that: d = 6. Area is πr² = 9π ≈ 28.27. Circumference is 2πr = 6π ≈ 18.85. Now invert the same disk: given A = 9π, r = √(A/π) = √9 = 3 and d = 2√(A/π) = 6. C = 2√(πA) returns 6π. Both directions describe one circle; area stays in square units and circumference in length units.
\[ A=\pi\cdot 3^{2}=9\pi,\quad r=\sqrt{9\pi/\pi}=3 \]
Frequently asked questions
How do I find the area of a circle?
Square the radius and multiply by π: A = πr². For r = 3 that is 9π ≈ 28.27. If you have the diameter instead, use A = πd²/4. This calculator does either from the Given menu.
What is the circumference formula?
Circumference of the rim is C = 2πr, or C = πd. At r = 3, C = 6π ≈ 18.85 length units. That is not the area of the disk.
How do I find the area of a circle from diameter?
Halve the diameter to get r, then use πr², which is the same as A = πd²/4. Diameter 6 is radius 3 and area 9π ≈ 28.27.
How do I find the radius from the area of a circle?
Take r = √(A/π). For the default area 9π ≈ 28.27, that square root is 3, and the diameter is 6. Set Given to Area to run the inverse on this page.
Can I use circumference as area?
No. At r = 3 the area is 9π ≈ 28.27 square units and the circumference is 6π ≈ 18.85 length units. They are different quantities: the shaded disk versus the rim. Treating 18.85 as an area (or 28.27 as a length) mixes units even when both formulas contain π.
How is a semicircle different from a full circle?
A semicircle is half the disk: area ½πr², and the perimeter is the curved arc plus the diameter. Use the Semicircle Area Calculator for that half-disk; this page is the full circle.
References
Assumptions and limitations
These circle results are unofficial. π is the same constant as JavaScript Math.PI. Length units on the input carry through: centimeters give area in cm² and circumference in cm.