How to Calculate Area: 10 Shapes, Formulas, Examples

By ZeroFee Tools · October 15, 2026 · 6 min read

Area answers a simple question: how much surface does this shape cover? Paint for a wall, carpet for a room, seed for a field and fabric for a project all start with an area calculation. The free Area Calculator from ZeroFee Tools handles ten shapes and converts between square feet, square meters, acres and hectares. This guide gives every formula with a worked example using real numbers, so you can follow along with a pencil or check the tool's answers by hand.

One rule governs every example below: area is always measured in square units. Square meters, square feet and square inches describe surfaces; plain meters and feet describe lengths. Keeping that distinction clear prevents the most common area mistakes before they start.

How do you calculate the area of a square or rectangle?

Square: side x side. Rectangle: length x width. A 5 m square covers 25 m², and a 6 m by 4 m rectangle covers 24 m².

These two formulas are the foundation of nearly all area work: floors, walls, lawns and fields are rectangles until proven otherwise. Measure both sides in the same unit, a frequent slip is mixing feet and inches, then multiply. The calculator accepts any of its supported units and converts the answer for you.

How do you calculate the area of a circle?

Multiply π by the radius squared: A = πr². A circle with radius 3 m has area π x 9, about 28.27 m². If you only have the diameter, halve it first, since the radius is half the diameter.

Why the radius squared? A circle of radius r fits inside a square of side 2r with area 4r², and the circle fills π/4 of that square. π is about 3.1416, and that is all the mystery there is. Round only at the end: keeping extra digits through the calculation protects the final answer.

How do you calculate the area of a triangle?

Multiply base by height and divide by 2. A triangle with base 8 m and height 5 m has area 20 m². If you know only the three sides, use Heron's formula instead.

The height must be perpendicular to the base you chose; for a right triangle it is simply the other short side. Heron's formula works from sides alone: for sides a, b and c, first compute s = (a + b + c) / 2, then area = sqrt(s(s-a)(s-b)(s-c)). With sides 5, 6 and 7 m: s = 9, and the area is sqrt(9 x 4 x 3 x 2) = sqrt(216), about 14.70 m². Surveyors love Heron because sides are easier to measure in the field than heights.

How do you calculate trapezoid, parallelogram and rhombus areas?

Trapezoid: average the two parallel sides and multiply by the height, (a + b) / 2 x h. Parallelogram: base x height. Rhombus: multiply the diagonals and divide by 2.

A trapezoid with parallel sides 10 m and 6 m and height 4 m: (10 + 6) / 2 x 4 = 32 m². A parallelogram with base 7 m and perpendicular height 3 m: 21 m². Note the height is measured at right angles to the base, not along the slanted edge; using the slant is the classic error here. A rhombus with diagonals 8 m and 6 m: (8 x 6) / 2 = 24 m². The diagonals of a rhombus always cross at right angles, which is why this formula works.

How do you calculate ellipse and circular sector areas?

Ellipse: π x a x b, where a and b are the two semi-axes. Sector: take the fraction of the full circle, (θ / 360) x πr². An ellipse with a = 5 m and b = 3 m covers about 47.12 m²; a 60° sector of radius 6 m covers about 18.85 m².

A circle is just an ellipse with a = b = r, so the circle formula drops out naturally. Sectors appear in sprinkler coverage, pie charts and pizza math: the 60° sector above is one-sixth of its circle, and one-sixth of π x 36 is 6π, about 18.85 m², which confirms the arithmetic.

How do you convert acres, hectares and square feet?

1 acre = 43,560 ft² = 4,046.86 m²; 1 hectare = 10,000 m², about 2.47 acres. A 1-acre lot is 4,046.86 m², and a 2-hectare field is about 4.94 acres.

Acres dominate US real estate, hectares dominate metric land measurement, and square feet dominate floor plans. Convert by multiplying: acres to square meters means x 4,046.86; square feet to acres means dividing by 43,560. The calculator does this in one step, including less common units like square inches and square kilometers.

How to calculate any area in 4 steps

1. Identify the shape. Match what you see to one of the ten shapes; an L-shaped room is two rectangles.
2. Measure in one unit. Take every measurement in the same unit before you calculate.
3. Apply the formula. Use the formulas above, or enter the numbers in the Area Calculator and let it do the arithmetic.
4. Convert if needed. Switch the answer to acres, hectares or square feet for whoever needs the number next.

6 practical tips

• Keep units consistent. A 10 ft by 8 ft room is 80 ft², but 10 ft by 96 in needs the inches converted first.
• Measure perpendicular heights. Triangle and parallelogram heights meet the base at a right angle; the slanted side is longer and gives a wrong answer.
• Confirm radius versus diameter. Halve a diameter before squaring it; using the diameter where the radius belongs quadruples the answer.
• Round last. Carry full precision through the multiplications and round only the final answer.
• Split irregular shapes. Divide L-shapes and odd plots into rectangles and triangles, total each, then add.
• Buy a little extra for real projects. Paint, carpet and turf need cuts and waste allowances, so round material orders up after calculating the exact area.

Frequently asked questions