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Area Calculator

Find the area of a square, rectangle, triangle, circle, sector, ellipse, trapezoid, parallelogram or regular polygon from its dimensions, plus the perimeter where it can be worked out.

  • Free, no sign-up
  • Runs in your browser
  • Math
All four sides are equal.
Use the same length unit for every field; the area comes out in that unit squared.

Read the guide How to Calculate Area: Formulas for Common Shapes

How to use the calculator

Choose a shape from the list. Only the measurements that shape needs are shown, for example length and width for a rectangle or radius and angle for a sector. Enter them and press Calculate.

The result card shows the area and, when the inputs are enough to work it out, the perimeter. The details panel shows the formula and every step with your numbers. Use one length unit for all fields: if the sides are in meters, the area is in square meters.

Formulas used

  • Square: A = s², perimeter 4s
  • Rectangle: A = l × w, perimeter 2(l + w)
  • Triangle (base and height): A = ½ × b × h
  • Triangle (three sides): Heron's formula A = √(s(s − a)(s − b)(s − c)), where s is half the perimeter
  • Circle: A = πr², circumference 2πr
  • Sector: A = (θ / 360°) × πr², perimeter 2r + rθ with θ in radians
  • Ellipse: A = πab, where a and b are the semi-axes
  • Trapezoid: A = ½ × (a + b) × h
  • Parallelogram: A = b × h
  • Regular polygon: A = n × s² / (4 × tan(180° / n)), perimeter n × s

Worked examples

Trapezoid. Parallel sides of 6 and 10 with a height of 4: A = ½ × (6 + 10) × 4 = 32.

Triangle from three sides. Sides 3, 4 and 5: s = (3 + 4 + 5) / 2 = 6, so A = √(6 × 3 × 2 × 1) = √36 = 6, and the perimeter is 12.

Regular hexagon. Six sides of 2: A = 6 × 2² / (4 × tan 30°) = 24 / 2.309401077 ≈ 10.39230485. The perimeter is 12.

Good to know

  • The height of a triangle, trapezoid or parallelogram is measured at a right angle to the base, not along a slanted side. Using the slanted side gives an area that is too large.
  • For a triangle given by base and height, a trapezoid or a parallelogram, the slanted sides are unknown, so no perimeter is shown.
  • An ellipse has no simple exact perimeter formula. The calculator uses an approximation by Ramanujan that is within about 0.04% even for a very flat ellipse.
  • Three lengths only make a triangle when the longest is shorter than the other two added together; otherwise you get an error.
  • This tool works out an area from a shape's measurements. To change an area you already have from one unit to another, such as acres to hectares, use the area converter instead.

Frequently asked questions

Why is no perimeter shown for some shapes?

The perimeter needs the length of every side. With only the base and height of a triangle, or the bases and height of a trapezoid, the slanted sides can have many different lengths, so the perimeter cannot be known. Use the three-sides triangle option when you know all sides.

What unit is the area in?

The area is in the square of whatever length unit you used. Sides in centimeters give square centimeters, and sides in feet give square feet. Do not mix units between fields.

How do I find the area of an irregular room or plot?

Split it into simple shapes such as rectangles and triangles, work out the area of each piece and add them up. Subtract any pieces that are cut out, such as a corner that does not belong to the room.

What is a regular polygon?

A polygon whose sides are all the same length and whose angles are all equal, such as an equilateral triangle, a square, a regular pentagon or a regular hexagon. The calculator also gives its apothem, the distance from the center to the middle of a side, and its interior angle.