Area Calculator
Compute the area of 16 shapes and tools. Pick a shape, enter dimensions, and get an instant result with a live labeled diagram, unit conversions, a cost estimator, and optional step-by-step working.
Composite shape builder
Stack any number of the 16 shapes above into one composite figure and get the combined total area, with a per-component breakdown. Ideal for L-shaped rooms, irregular lots, and floor plans that are really several simple shapes glued together.
What is area?
Area is the amount of flat, two-dimensional space a shape covers. Think of it as the size of a surface — the floor of a room, a garden bed, a piece of land, a sheet of glass, or a screen. If you were painting that surface, the area tells you exactly how much paint you would need to cover every part of it.
Because area measures space in two directions at the same time (length and width), the answer is always in square units — square centimeters, square meters, square feet, acres, hectares and so on. A number without a unit is not an area; “12” only becomes meaningful when you say 12 m² or 12 ft².
Every formula on this page is really the same idea in different clothing: find how far the shape stretches sideways, multiply by how far it stretches up and down, then adjust for curves, slopes or missing corners. Rectangles use plain length × width. Triangles use half of that because a triangle is exactly one half of a matching rectangle. Circles use π because the width and height blend smoothly around the curve.
Area formulas explained, shape by shape
For every shape below you'll see a plain-English explanation, the formula (with what each letter means), a diagram, and a worked example — all in one place.
Square
A square has four equal sides meeting at right angles. A = s² just multiplies the side by itself — the square is s wide and s tall, so it covers s × s unit tiles. Use it for square tiles, chessboards, or a square patio slab.
Rectangle
A rectangle has two pairs of equal, parallel sides and four right angles. A = l × w counts how many 1×1 tiles fit inside: length rows of width tiles. Handy for room floors, TV screens, garden beds, or a sheet of plywood.
Triangle (base–height)
The base–height form A = ½ b h works because a triangle is exactly half the rectangle drawn around its base and perpendicular height. Use it for sail panels, roof gables, or any triangle where you can measure a base and its height.
Triangle (Heron's formula, three sides)
When you only know the three side lengths, Heron's formula finds the area without needing any angle. First compute the semi-perimeter s, then plug in. Great for land plots surveyed by side lengths.
Trapezoid
A trapezoid has one pair of parallel sides (the bases). A = ½ (b₁ + b₂) h averages the two bases and multiplies by the perpendicular distance — geometrically it's the rectangle you'd get if both bases had the same length. Useful for drainage channels, retaining walls, and irregular fields.
Parallelogram
A parallelogram has two pairs of parallel sides but not necessarily right angles. A = b × h uses the base and the perpendicular height (not the slanted side): slice a triangle off one end, slide it to the other, and you get a rectangle of the same area.
Rhombus
A rhombus is a parallelogram with all four sides equal — a "pushed-over square." Its diagonals meet at right angles and split it into four congruent right triangles, so A = ½ d₁ d₂. Comes up in diamond-pattern tiling and kite-shaped windows.
Kite
A kite has two pairs of adjacent equal sides — the classic flying-kite outline. Its diagonals are perpendicular, so the same ½ d₁ d₂ formula works. Use it when designing an actual kite or cutting a diamond-shaped patch.
Circle
A circle is the set of all points a fixed distance r from a centre. A = π r² can be pictured by slicing the circle into thin wedges and rearranging them into a near-rectangle of width π r and height r. Everywhere: round tables, pizzas, pipes, wheels, sprinkler coverage.
Semicircle
A semicircle is exactly half a circle, cut along a diameter — so its area is half the circle's. Useful for arched doorways, half-round windows, garden arches, and the ends of a running track.
Sector (pie slice)
A sector is a pie slice of a circle — two radii and the arc between them. A = ½ r² θ (with θ in radians) is just the circle's area scaled by the fraction of the full turn the sector covers.
Circular segment
A segment is the thin region between a chord and the arc it cuts off — the sector minus the triangle formed by the two radii. That's exactly what ½ r² (θ − sin θ) computes. Comes up in tank-fill problems and bridge arches.
Ellipse
An ellipse is a stretched circle with two axes: the semi-major a (longer) and semi-minor b (shorter). A = π a b generalizes π r² — when a = b it collapses back to a circle. Use for oval running tracks, planetary orbits, and oval tabletops.
Regular polygon
A regular polygon has n equal sides and equal angles — think hexagons, octagons, pentagons. The formula comes from splitting it into n identical isosceles triangles from the centre and adding them up. Useful for hex tiles, stop-sign panels, and gazebo floors.
Irregular polygon (by coordinates)
An irregular polygon has no requirement of equal sides or angles — just a list of vertices in order. The Shoelace formula sums signed cross-products of consecutive vertices, which geometrically adds and subtracts triangle slices until only the enclosed area remains. Perfect for land surveys, GIS parcels, and floor plans.
Annulus (ring)
An annulus is a flat ring — the region between two concentric circles of radius R (outer) and r (inner). Its area is the big circle minus the hole. Use for washers, pipe cross-sections, and running-track lanes.
Regular star polygon
A regular star polygon has n identical points arranged around a centre. Slice it into 2n congruent triangles — each with two sides R and r meeting at an angle of π/n — and add them up to get A = n × R × r × sin(π/n). Use for star cutouts, logos, badges and decorative tiling.
Common area unit conversions
| From | To | Multiply by |
|---|---|---|
| 1 square meter | square feet | 10.7639 |
| 1 square meter | square yards | 1.19599 |
| 1 square foot | square meters | 0.09290 |
| 1 acre | square meters | 4046.856 |
| 1 acre | hectares | 0.40469 |
| 1 hectare | square meters | 10 000 |
| 1 hectare | acres | 2.47105 |
| 1 square mile | square kilometers | 2.58999 |
| 1 square kilometer | square miles | 0.38610 |
Features of this calculator
- 16 shapes and tools — square, rectangle, triangle (base–height and Heron), trapezoid, parallelogram, rhombus, kite, circle, semicircle, sector, circular segment, ellipse, regular polygon (any n ≥ 3), irregular polygon by coordinates (Shoelace), annulus, and regular star polygon (A = n × R × r × sin(π/n)).
- Dropdown shape picker with a distinct input form for each shape — only the fields that shape actually needs.
- Live SVG diagram that updates as you type, with your dimensions labeled — the SSS triangle draws to scale from the actual side lengths, and the coordinate polygon plots your vertices.
- Triangle mode toggle: base–height, or three-sides (Heron's formula). The circular-segment tool also toggles between central-angle and chord-length input.
- Sector and circular-segment angles accept both degrees and radians via a unit toggle.
- Length unit selector (mm, cm, m, km, in, ft, yd, mi) that feeds the automatic unit-conversion output.
- Every result also shown converted to square meters, square feet, square yards, acres, hectares, square kilometers and square miles.
- Perimeter/circumference reported alongside the area wherever it's well-defined for the chosen shape.
- Cost / material estimator on every shape — enter a price per square unit and get an instant total for flooring, paint, land or carpet.
- Polygon by coordinates: paste any set of (x, y) vertices and the Shoelace formula does the rest — with a per-edge cross-term breakdown.
- Show/hide step-by-step working — formula, substitution, and final answer for every shape, with a variable legend under every formula.
- Copy the result, download it as a PNG or PDF, or print the result panel — all from the results toolbar.
- Input validation with clear error messages — negative sides, triangle-inequality violations, chord longer than the diameter, etc.
- Trapezoid alternate input mode: enter all 4 side lengths (both bases plus the two non-parallel sides) and the calculator derives the height for you, with a fallback for the parallelogram edge case.
- Composite shape builder: stack any number of the 16 shapes into one figure and get the combined total area, a per-component breakdown table, and each component's percentage share — great for L-shaped rooms, irregular lots, and floor plans.
Frequently asked questions
+What is area?
Area is the amount of two-dimensional space a flat shape covers. It's measured in square units — square meters, square feet, acres, hectares and so on.
+How do I find the area of a triangle when I only know its three sides?
Use Heron's formula. Compute the semi-perimeter s = (a + b + c) / 2, then the area is √[s(s − a)(s − b)(s − c)]. This calculator does both this and the standard ½ × base × height version.
+What's the formula for a regular polygon's area?
For a regular polygon with n sides of length s, the apothem is a = s / (2 tan(π/n)) and the area is A = ½ × perimeter × apothem = ¼ × n × s² × cot(π/n). This calculator works for any n ≥ 3.
+How do I calculate the area of a ring (annulus)?
Subtract the inner circle from the outer circle: A = π(R² − r²), where R is the outer radius and r is the inner radius.
+How is the area of a regular star polygon calculated?
For a regular star with n points, outer radius R (centre-to-tip) and inner radius r (centre-to-notch), the area is A = n × R × r × sin(π/n). The star splits into 2n congruent triangles, each with two sides R and r meeting at an angle of π/n, and this formula adds them up.
+What units does the calculator use?
Any consistent unit — enter all dimensions in the same unit and the answer is in the square of that unit. Every result is also shown converted to square feet, square meters, square yards, acres and hectares for quick reference.
+Can I enter the angle of a sector in radians?
Yes — the sector shape has a degrees/radians toggle. Full circle = 360° = 2π rad.
+How is the area of an irregular polygon computed?
From its vertices (x, y) using the Shoelace formula: A = ½ |Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. The Polygon (Coordinates) tool applies this to any number of vertices, in any order, closed or open.
+How is a circular segment different from a sector?
A sector is the pie-slice bounded by two radii and an arc. A segment is bounded by a chord and its arc — it's the sector with the central triangle removed. Area = ½ r² (θ − sin θ).
+Can I estimate cost from the area?
Yes — enter a price per square unit in the Cost estimator that appears with every result. It multiplies the computed area by that price so you can quickly estimate flooring, paint, land or carpet totals.
+How do I find a trapezoid's area if I only know all four side lengths?
Switch the trapezoid tool to "All 4 sides" mode and enter both bases (b₁, b₂) and the two non-parallel sides (c, d). The calculator finds x = [(b₂ − b₁)² + c² − d²] / [2(b₂ − b₁)], then the height h = √(c² − x²), and finally A = ½(b₁ + b₂)h. If b₁ equals b₂ the shape is a parallelogram and h = c.
+How does the composite shape builder work?
Add as many components as you need, each using any of the 16 supported shapes, and the calculator sums their individual areas into one combined total. It also shows a breakdown table with each component's area and percentage share — useful for L-shaped rooms, irregular lots, and multi-part floor plans.