Square Inches of a Circle Calculator

Enter a circle's radius or diameter to get its area in square inches (A = πr²), plus the area in your chosen unit, circumference, and both dimensions converted to inches.

Quick Facts

Area (from radius)
A = π × r²
Radius in inches gives area directly in square inches.
Area (from diameter)
A = π × (d/2)² = (π/4) × d²
Halve the diameter to get the radius first.
Circumference
C = 2 × π × r = π × d
Distance around the circle, same units as radius/diameter.
Unit conversion
1 ft² = 144 in²
Divide square inches by 144 to get square feet.

Your Results

Calculated
Area (Square Inches)
-
A = π × radius², converted to inches
Area (Your Unit²)
-
Same area expressed in the unit you entered
Circumference
-
C = 2πr, in inches and your unit
Radius / Diameter Used
-
Both dimensions converted to inches

Ready

Enter a radius or diameter and a unit, then press Calculate.

Formula and Method for the Square Inches of a Circle

The area of a circle is found with A = π × r², where r is the radius and π (pi) is approximately 3.14159. When the radius is measured in inches, this formula gives the area directly in square inches — which is what "square inches of a circle" usually means: how much surface area a circular shape covers, expressed in in². If you only know the diameter (the distance across the circle through its center), divide it by 2 to get the radius, or use the equivalent form A = π × (d/2)² = (π/4) × d².

How the calculation works

Enter either the radius or the diameter, choose the unit it's measured in, and this calculator converts that value to inches first. It then squares the radius and multiplies by π to get the area in square inches, and also reports the same area in the square of whatever unit you originally entered (for example, ft² if you entered feet). The circumference — the distance around the circle — is calculated separately as C = 2 × π × r, which equals π × d.

Common mistakes

  • Radius vs. diameter: plugging the diameter into A = πr² instead of A = π(d/2)² produces an area four times too large. Always confirm which measurement you have before calculating.
  • Mixing units: a radius of "6" only means something once you attach a unit. Convert everything to one unit (this calculator does that automatically once you pick a unit) before comparing or adding areas.
  • Square inches vs. square feet: 1 ft² equals 144 in², not 12 in² — because both the length and width factors of 12 multiply together (12 × 12 = 144).

Real-world applications

  • Sizing round tabletops, pizzas, or fabric circles, where material or toppings are priced per square inch or square foot
  • Cutting circular gaskets, washers, or panels from sheet stock, where area determines material usage and cost
  • Estimating paint or coating needed for a circular surface such as a tank lid or manhole cover
  • Comparing pipe, duct, or drain cross-sectional areas, which are always circular (or approximately so) and reported in square inches

Frequently Asked Questions

What is the formula to find the square inches of a circle?
Multiply π (about 3.14159) by the radius squared: A = π × r², where the radius is measured in inches. If you only know the diameter, divide it by 2 first to get the radius, or use A = π × (d/2)².
How do I find the area of a circle using its diameter instead of radius?
Use A = π × (d/2)², which is the same as A = (π/4) × d². For example, a circle with a 12-inch diameter has an area of π × 6² ≈ 113.1 square inches.
How do I convert square inches to square feet?
Divide the area in square inches by 144, since 1 square foot equals 12 × 12 = 144 square inches. A circle with an area of 452.4 in² covers about 3.14 ft².
Does this calculator work with units other than inches?
Yes. Enter the radius or diameter in inches, feet, centimeters, millimeters, meters, or yards — the calculator converts your value to inches internally and reports the area in both square inches and the square of your chosen unit.

Related calculators