Quarter Circle Area: Formula & Calculator

This calculator works out the area of a quarter circle when you enter its radius. You get the area in square units, plus the same value in square meters and square feet for convenience. The formula is the standard one: one-fourth of the area of a full circle.

Formula

The area of a quarter circle is exactly one-fourth of the area of a full circle with the same radius. The formula is:

A = (π × r²) / 4

• A — area of the quarter circle (square units, e.g., m², cm², ft²)
• π (pi) — approximately 3.14159
• r — radius of the circle (same unit as the area’s linear dimension, e.g., m, cm, ft)

If you know the diameter instead of the radius, remember that r = d/2. You can also write the formula using diameter: A = (π × d²) / 16.

Worked Example

Using the default values from the calculator above (radius = 5 m):

1. Square the radius: r² = 5² = 25 m²
2. Multiply by π: 25 × 3.14159 = 78.53975 m² (this is the full circle area)
3. Divide by 4: 78.53975 / 4 = 19.63494 m²
4. Rounded to two decimals: 19.63 m²

To get square feet, multiply the square-meter result by 10.7639: 19.63 × 10.7639 ≈ 211.3 ft². (The calculator shows 211.28 ft² when rounded.)

When to Use This

Quarter circles appear in many real‑life situations: a quarter‑round garden bed, a pie‑slice shape, a curved corner of a room, a semicircular driveway divided in half, or any object that is exactly one quarter of a full circle. You use this formula whenever you need the area of a shape that is bounded by two perpendicular radii and the arc between them.

The result tells you how much surface that quarter‑circle covers. For example, if you are ordering sod for a quarter‑circle lawn, the area tells you how many square meters (or square feet) of sod to buy. If you are painting a quarter‑circle wall decoration, the area tells you how much paint to get (though you also need to know the paint’s coverage per liter or gallon).

Common Mistakes

• Using the diameter instead of the radius. The formula requires the radius. If you have the diameter, halve it first. Forgetting to halve gives an area four times larger than correct.
• Forgetting to divide by 4. The whole circle area is πr²; the quarter is that divided by 4. Skipping the division yields the full circle area.
• Mixing units. If you enter the radius in meters, the area will be in square meters. If you enter in feet, the area is in square feet. Do not combine meters with centimeters without converting.
• Rounding too early. If you round π to 3.14 and also round intermediate results, the final answer can be off by a few percent. Keep extra digits until the end.
• Using the wrong pi. Some calculators have a π button; using 3.14 is fine for rough work but for precise results use the built-in π.

Tips

• If you have the diameter, use the formula A = (π × d²) / 16 to avoid an extra step.
• For a quick mental estimate, use π ≈ 3.14 and round the radius to one decimal. That gives a good approximation for most everyday purposes.
• When converting between square units, remember that 1 m² = 10.7639 ft² and 1 ft² = 0.092903 m². The calculator does this for you.
• If you are measuring a physical object, measure the radius from the center point to the outer edge along a straight line. Make sure the two straight sides are exactly perpendicular (90°).
• For a semicircle (half circle), use A = (πr²)/2; for a three‑quarter circle, use A = (3πr²)/4.

Troubleshooting

My result seems too small or too large. Check that you entered the radius, not the diameter. Double‑check the unit: a radius of 5 cm gives a much smaller area than 5 m. Also verify that you divided by 4.

The calculator shows “NaN” or an error. This usually means the radius is zero or negative. Enter a positive number. A radius of zero gives an area of zero, which is mathematically correct but not useful.

I have the diameter, not the radius. Divide the diameter by 2 first, then use the formula. Or use the diameter version of the formula.

I need the area in a different unit. Convert the radius to the desired unit first, then compute the area. For example, to get square inches from a radius in feet, multiply the radius by 12 to get inches, then square and multiply by π/4.

My shape is not a perfect quarter circle. The formula only works for an exact 90° arc. If the angle is different, you need the sector area formula: A = (θ/360) × πr², where θ is the angle in degrees.

Frequently Asked Questions

What is the formula for the area of a quarter circle?
The area is A = (πr²)/4, where r is the radius. It is exactly one fourth of the full circle’s area.

How do I find the area if I only know the diameter?
Use A = (πd²)/16, because d = 2r. For example, a diameter of 10 m gives r = 5 m, and the area is (π × 25)/4 ≈ 19.63 m².

What is the perimeter of a quarter circle?
The perimeter (or circumference of the curved part plus the two straight sides) is (πr)/2 + 2r. The curved arc length is one quarter of the full circumference: (2πr)/4 = (πr)/2.

Can I use this formula for a semicircle?
No. A semicircle is half a circle, so its area is (πr²)/2. A quarter circle is exactly half of a semicircle.

What if the radius is in inches and I want square feet?
Convert the radius to feet first (divide by 12), then compute the area in square feet. Or compute the area in square inches and divide by 144 (since 1 ft² = 144 in²).

Why is π used in the formula?
π is the constant that relates a circle’s circumference to its diameter. It appears in any circle‑area formula because the area of a full circle is πr². The quarter circle inherits that constant.

Related

• Miles to Ft Converter & Formula
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• Area of Circle Calculation & Formula

in r | Radius | m | 5 | 0
out area | Area | m² | (pi * r^2) / 4 | 2
out area_ft | Area (sq ft) | ft² | (pi * r^2) / 4 * 10.7639 | 2