Math & Science
Area Calculator
Area for eight shapes, including a triangle from three sides using Heron’s formula.
Area Calculator
About the Area Calculator
Eight shapes, each with the inputs it actually needs. Circle, rectangle, square, triangle, trapezoid, parallelogram and ellipse are all here, plus a second triangle mode that works from three side lengths using Heron's formula — useful when you can measure the sides but not the height.
Pick a shape and the form changes to ask only for the dimensions that shape requires. You get the area, the perimeter where it can be determined, and the formula that was applied, so the working is visible rather than hidden.
Units are whatever you put in. Enter centimetres and the area comes back in square centimetres; enter feet and you get square feet. Just keep every dimension in the same unit — mixing them is the most common source of a wrong answer.
How to use the Area Calculator
- Choose a shape. The fields change to suit it.
- Enter the dimensions in any consistent unit.
- For a triangle, use base and height if you have them, or three sides if you do not.
- Select Calculate area.
- Perimeter is shown where the inputs are enough to determine it.
Area formula and perimeter formula for every shape
| Shape | Area | Perimeter |
|---|---|---|
| Circle | A = πr² | C = 2πr |
| Rectangle | A = l × w | P = 2(l + w) |
| Square | A = s² | P = 4s |
| Triangle (base & height) | A = ½bh | Not determinable |
| Triangle (three sides) | Heron's formula | P = a + b + c |
| Trapezoid | A = ½(a + b)h | Needs all four sides |
| Parallelogram | A = bh | Needs the slant side |
| Ellipse | A = πab | No exact simple formula |
| Semicircle | A = ½πr² | P = πr + 2r |
| Rhombus | A = d₁ × d₂ ÷ 2 | P = 4s |
Worked example
A circular patio has a radius of 2.4 metres. How much paving does it need?
A = πr² = π × 2.4² = π × 5.76
18.10 square metres
Order matters here. Square the radius first, then multiply by π. Multiplying 2.4 by π and then squaring gives 56.8 — more than three times too big.
Finding a triangle's area from three sides
When you can measure all three sides but not the perpendicular height, Heron's formula solves it. Start with the semi-perimeter, then feed it in:
s = (a + b + c) ÷ 2
A = √[ s(s − a)(s − b)(s − c) ]
s is the semi-perimeter — half the way round the triangle.
For a triangle with sides 5, 6 and 7: s = 9, so A = √(9 × 4 × 3 × 2) = √216 = 14.70. No height needed anywhere.
Three lengths only form a triangle if the two shorter ones add to more than the longest — the triangle inequality. Sides of 2, 3 and 9 cannot close, and Heron's formula returns a negative under the square root to tell you so.
Why some shapes give an area but no perimeter
A triangle described by its base and height does not have a fixed shape. Slide the apex sideways and the area stays identical while the two slanted sides change length. Infinitely many triangles share one base and height, so the perimeter is genuinely unknown from that information.
The same applies to a parallelogram given base and height, and a trapezoid given its two parallel sides and height. To get a perimeter you need the actual side lengths. The ellipse is a different case: its perimeter has no exact formula in elementary functions at all, only approximations such as Ramanujan's.
Converting between area units
| From | To | Multiply by |
|---|---|---|
| Square inches | Square feet | ÷ 144 |
| Square feet | Square metres | 0.092903 |
| Square metres | Square feet | 10.7639 |
| Square feet | Square yards | ÷ 9 |
| Square metres | Hectares | ÷ 10,000 |
| Acres | Square feet | 43,560 |
Area conversion factors are the square of length factors. One foot is 12 inches, but one square foot is 144 square inches, not 12. Forgetting to square the factor is the single most common unit error in area work.
Sq ft calculator: working out square footage for a room
Multiply length by width for a rectangular room. For an L-shape, split it into two rectangles, work out each, and add them. For anything with a curved edge, treat the curve as part of a circle and use πr² scaled to the fraction you have.
Add 5–10% for waste when buying flooring or tile — cuts and breakages are certain. For volume rather than area, use the volume calculator.
Square footage calculator with feet and inches
Rooms are rarely a neat number of feet. Turn inches into a decimal of a foot first — divide by 12. Then multiply length by width.
Worked example
A room is 12 ft 6 in by 10 ft 9 in.
12 ft 6 in = 12.5 ft. 10 ft 9 in = 10.75 ft.
12.5 × 10.75 = 134.4 square feet
Buying flooring or tiles? Add 5–10% for cuts and waste.
Area of irregular shapes
An L-shaped room or an odd garden is just a few simple shapes stuck together.
- Sketch the space and split it into rectangles, triangles or circles.
- Find each area with the calculator above.
- Add them up. Subtract any cut-outs, such as a kitchen island.
Area unit conversions
| To convert | Do this | Example |
|---|---|---|
| Square inches → square feet | ÷ 144 | 720 in² = 5 ft² |
| Square feet → square inches | × 144 | 3 ft² = 432 in² |
| Square feet → square yards | ÷ 9 | 180 ft² = 20 yd² |
| Square feet → square metres | × 0.0929 | 100 ft² = 9.29 m² |
| Square metres → square feet | × 10.764 | 20 m² = 215.3 ft² |
| Square feet → acres | ÷ 43,560 | 21,780 ft² = 0.5 acre |
Square feet to cubic yards (mulch, soil, concrete)
Square feet measure a flat area. Cubic yards measure volume, so you need a depth too.
Cubic yards = square feet × depth in feet ÷ 27
A 12 ft × 10 ft bed covered 4 inches deep: 120 × (4 ÷ 12) ÷ 27 = 1.48 cubic yards. For full 3D shapes, use the volume calculator.
Common geometry formulas in words
- Trapezoid formula: area = half the sum of the parallel sides × height. Sides 6 and 10, height 4: ½ × 16 × 4 = 32.
- Area of a parallelogram formula: base × perpendicular height, not the slanted side.
- Area of rhombus formula: multiply the two diagonals and halve it. Diagonals 8 and 6 give 24.
- Circle circumference formula: C = 2πr, or πd. The circle perimeter formula is the same thing.
- Diameter of a circle formula: d = 2r, or d = C ÷ π when you only know the circumference.
- Semicircle area formula: ½πr². Radius 4: about 25.1.
- Formula for perimeter: add all the sides. For a rectangle that is 2 × (length + width).
Acreage calculator: square footage of an acre
One acre is 43,560 square feet, or about 4,047 square metres. To convert acres to square feet, multiply by 43,560. To get acreage from square feet, divide by 43,560.
A 100 × 200 ft lot is 20,000 sq ft, which is 20,000 ÷ 43,560 = 0.46 acres. A quarter-acre lot is 10,890 sq ft.
Square yard calculator and sq ft to linear ft
- Square feet to square yards: divide by 9. A 12 × 15 ft room is 180 sq ft, or 20 square yards of carpet.
- Sq ft to linear ft: divide the area by the width of the material in feet. 120 sq ft of 6-inch (0.5 ft) boards needs 120 ÷ 0.5 = 240 linear feet.
- Area of a circle with diameter: A = πd² ÷ 4, so you never need to halve the diameter first.
Other ways to use this calculator
Area questions come in many forms. This calculator covers them once you pick the right shape.
- Area of a circle calculator — pick Circle and enter the radius.
- Trapezoid calculator — pick Trapezoid and enter both parallel sides and the height.
- Perimeter calculator — the perimeter shows next to the area for every shape that has one.
- Surface area calculator — for 3D shapes, the volume calculator gives surface area too.
- Semicircle area calculator — use Circle, then halve the area.
- Area of an oval calculator — pick Ellipse and enter the two half-widths.
- Roof square footage calculator — find the floor-plan area, then multiply by your roof pitch factor (about 1.12 for a 6/12 pitch).
- Yard and room square footage calculator — split the space into rectangles and triangles and add them up.
- Square meters calculator — work in metres and the result is in square metres.
- Rectangle area and circle area — choose the shape and enter the sides or radius.
- Trapezoid area and ellipse area — both are in the shape list with their own formulas.
Related guides
Frequently asked questions
The area of a circle is A = πr² — pi times the radius squared. For a radius of 2.4 m: 2.4² = 5.76, and 5.76 × π = 18.10 square metres. Square the radius before multiplying by π. If you have the diameter instead, halve it first, since using the diameter in place of the radius makes the answer four times too large.
Use Heron's formula. Add the three sides and halve the total to get the semi-perimeter s, then take the square root of s(s−a)(s−b)(s−c). For sides 5, 6 and 7, s is 9, giving √(9×4×3×2) = √216 = 14.70. No height is needed. If the two shorter sides do not add to more than the longest, the triangle cannot exist.
Whichever you enter. The calculator does not assume a unit — put in centimetres and the area comes back in square centimetres, put in feet and you get square feet. The one rule is to keep every dimension in the same unit. Mixing metres and centimetres in one shape is the most common cause of a wrong answer, and nothing in the maths will warn you.
Because base and height do not fix the shape. Slide a triangle's apex sideways and the area stays the same while the slanted sides get longer or shorter, so infinitely many triangles share one base and height. The perimeter is genuinely unknowable from that information — you need the actual side lengths. The same is true of a parallelogram given only base and height.
Multiply the length by the width, both in feet. Convert inches to feet first by dividing by 12. A room 12 ft 6 in by 10 ft 9 in is 12.5 × 10.75 = 134.4 square feet.
Divide by 144, because one square foot is 12 inches by 12 inches. 720 square inches is 720 ÷ 144 = 5 square feet.
An acre is 43,560 square feet. Multiply acres by 43,560 to get square feet, or divide square feet by 43,560 to get acres. A 20,000 sq ft lot is about 0.46 acres.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — area units and conversion factors
- Heron's formula — deriving triangle area from three sides
- Area — Encyclopaedia Britannica — definitions and standard geometric formulas