Area Calculator

AREA FORMULA GEOMETRY MATH SHAPES

By RECATOOLS Editorial Checked against sources by Jeffrey Tan, Founder & Architect, RECATOOLS Published 6 Jun 2026 Updated 19 Oct 2026 Last reviewed 19 Oct 2026

About this tool

Calculate the area of any shape — rectangle, circle, triangle, trapezoid and more — with formulas shown.

Calculate the area of any shape — rectangle, circle, triangle, trapezoid, rhombus, ellipse and regular polygon — with formulas shown. Convert m² to sq ft and acres. Free.

RT-CNV-072 · Converters & Units

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Unit:

Length (cm)

Width (cm)

How to Use the Area Calculator

Select your shape

Click one of the 8 shape buttons: Rectangle, Circle, Triangle, Parallelogram, Trapezoid, Rhombus, Ellipse, or Regular Polygon. The input fields below will update to match the selected shape's required measurements.

Enter your measurements

Type in the required values for your shape. For circles, toggle between radius and diameter input. For triangles, toggle on Heron's formula to compute area from three side lengths (useful when you don't know the height).

See results instantly

Area and perimeter update live as you type. The formula line shows the exact equation used with your numbers substituted in — great for checking homework or understanding the calculation.

Check the unit conversions

The secondary row converts your result to m², square feet and acres using the exact definitions (1 ft = 0.3048 m; 1 acre = 43,560 sq ft). That is handy for flat sizes quoted in square metres beside listings quoted in square feet, and for land quoted in acres.

Area — The Foundation of Geometry, Architecture and Real Estate

Area and perimeter

Area is the measurement of a two-dimensional surface — the amount of space enclosed within a boundary, in square units. Perimeter is the length of that boundary, in linear units. Mixing them up is one of the commonest slips in school mathematics. A rectangle that is 10 cm by 5 cm has an area of 50 cm² and a perimeter of 30 cm — two different quantities answering different questions. This calculator shows both wherever the inputs determine both.

The circle's area comes from π, and π's first good bounds come from Archimedes of Syracuse (287–212 BC). In Measurement of a Circle he fitted regular polygons of 96 sides inside and outside a circle and showed that π lies between 3 10/71 and 3 1/7. The upper bound, 22/7, is still taught today and is within 0.04% of π. His method of exhaustion — trapping a curved area between two straight-sided ones — is the idea integral calculus later made general.

Floor areas in Singapore: square metres and square feet

HDB flats are described in square metres, while many property listings quote square feet, so the conversion comes up constantly. The exact factor is 1 m² = 10.7639 sq ft (1 ÷ 0.09290304). In the most recent 5,000 resale transactions of each flat type published on data.gov.sg (to October 2026), the median floor area was 67 m² (about 721 sq ft) for a 3-room flat, 93 m² (about 1,001 sq ft) for a 4-room flat and 117 m² (about 1,259 sq ft) for a 5-room flat. Individual flats vary widely around those medians, so measure your own.

"Area is measured in square units and perimeter in plain ones — a rectangle 10 cm by 5 cm encloses 50 cm² inside a 30 cm boundary."

For flooring, measure each room (the Rectangle shape covers most of them), add the areas, and then add an allowance for offcuts and breakage — your supplier or contractor will say how much for the tile or plank you have chosen. A 10% allowance on 90 m² is 99 m²; a 15% allowance is 103.5 m². For a bay window or an angled wall, the trapezoid or parallelogram shapes may give a closer figure than a rectangle.

Land in Singapore is scarce enough that the country has measured its own growth: the island's land area was 744.3 km² at the end of 2025, up from 581.5 km² in 1965 — about 163 km² added, largely by reclamation (Singapore Department of Statistics).

Why π never ends — and why that matters for area

π appears in the area formula of every curved shape here — circles and ellipses — and regular polygons with many sides approach a circle's area. π is irrational, so its decimal expansion never repeats or ends; every area that uses it is computed to the precision of the device, not exactly.

The intuition behind the circle formula: cut a circle into many thin slices and lay them head to tail, and they approach a rectangle whose base is half the circumference (πr) and whose height is the radius (r), so the area is πr × r = πr². Area grows with the square of length, so a pizza 30 cm across has four times the area of one 15 cm across, not twice.

The ellipse is the one shape here whose perimeter has no simple formula. The calculator evaluates it exactly (to the precision of your device) through the complete elliptic integral, using the arithmetic-geometric mean. The shortcut 2π√((a² + b²)/2), which this page used before, overstates the perimeter by 1.3% for semi-axes of 8 and 5, and by almost 10% for 10 and 1.

Doubling a pizza quadruples it, and Archimedes got there before calculus

Archimedes (287–212 BC) used the method of exhaustion — the forerunner of integral calculus — to trap π between 3 10/71 and 3 1/7 with 96-sided polygons, over 1,900 years before Newton.

Singapore's land area was 744.3 km² at the end of 2025, per the Department of Statistics.

The median 4-room HDB resale flat in recent data.gov.sg records is 93 m² (about 1,001 sq ft); the 3-room median is 67 m² and the 5-room 117 m².

If you double a pizza's diameter, the area quadruples — a 30 cm pizza has 4× the area of a 15 cm pizza, not twice as much.

Heron of Alexandria (c. 10–75 AD) gave the triangle area formula from three sides alone in his Metrica.

Singapore's land area grew from 581.5 km² in 1965 to 744.3 km² in 2025 — about 163 km² more, largely reclaimed from the sea.

A circle always encloses more area than a square with the same perimeter — for a 28 cm perimeter, a circle gives 62.4 cm² (28² ÷ 4π) versus 49 cm² for a square.

A regular polygon's area creeps toward the circle's as its sides increase — a hexagon covers 82.7% of the circle drawn round it, a 12-sided polygon 95.5%.

The ellipse formula πab is the circle's πr² with the radius split in two — set a = b and it becomes the circle again.

1 acre = 43,560 sq ft = 4,046.856 422 4 m² exactly, since the international foot replaced the U.S. survey foot for land measure at the start of 2023 — about 0.405 hectare.

📅 Research current as of 19 Oct 2026 · Sources: Exact unit definitions from NIST SP 811 Appendix B.8 and the Federal Register notice of 5 October 2020 (acre = 43,560 ft²); ellipse perimeter by the complete elliptic integral (DLMF 19.8, 19.9); Singapore land area from SingStat table M890151; HDB floor-area medians from data.gov.sg resale records to October 2026. Calculated in your browser.

Standards, published formulas, and reference data are revised over time — check against a current authoritative source before relying on these figures.

Frequently Asked Questions

The area of a circle is A = π × r², where r is the radius (half the diameter) and π ≈ 3.14159. If you know the diameter (d) instead, use r = d/2 first. This calculator accepts either radius or diameter — toggle the "enter diameter" option after selecting the Circle shape.
Heron's formula calculates the area of a triangle when you know all three side lengths (a, b, c) but not the height. First find the semi-perimeter: s = (a + b + c) / 2. Then the area is: A = √(s(s−a)(s−b)(s−c)). It is named for Heron of Alexandria (c. 10–75 AD), who gave it in his Metrica.
Area is the amount of 2D space enclosed within a shape, measured in square units (cm², m², ft²). Perimeter is the total length of the boundary around the shape, measured in linear units (cm, m, ft). A rectangle 10 × 5 cm has area 50 cm² and perimeter 30 cm. Area is used for flooring, painting and land; perimeter is used for fencing, framing, and edging.
Divide by 0.09290304, the exact number of square metres in a square foot — the same as multiplying by about 10.7639. So 90 m² is 968.75 sq ft. To go the other way (sq ft to m²), multiply by 0.09290304. This calculator shows automatic conversions to m², sq ft, and acres in the results row — useful for comparing HDB flat sizes quoted in different units.
Use Heron's formula when you have all three side lengths but cannot easily measure or calculate the perpendicular height. This is common in land surveying, architecture, and exam problems where only side measurements are given. The standard ½ × base × height formula is simpler when you have the height — use whichever fits your available data.
The standard approach is to divide the irregular shape into simpler shapes (rectangles, triangles, semicircles) and sum their areas. This is the composite figures method taught in Singapore's primary and secondary curriculum. For each component, use this calculator, then add the results together. For very irregular shapes (e.g. land plots), surveyors use the coordinate geometry method (Shoelace formula).
A regular polygon has n equal sides of length s. The area formula is: A = (n × s² × cot(π/n)) / 4. This is equivalent to dividing the polygon into n isosceles triangles from the centre and summing their areas. Select "Reg. Polygon" in this calculator and enter the number of sides and side length — it handles the trigonometry automatically.
Measure each room's length and width in metres, calculate the area of each (use the Rectangle shape), and sum the room areas. Subtract areas for built-in wardrobes or wet areas you won't tile. Then add an allowance for offcuts and breakage — ask your supplier what they recommend for the material you have chosen; for a 12% allowance, multiply the total area by 1.12.
Use whatever unit matches your measurements. For room-scale renovation (HDB, condo), use m for metres. For crafts and small objects, use cm. For engineering drawings, use mm. For land and property, use m or ft, whichever your plan is drawn in. The unit conversion row shows your result in m², ft² and acres regardless of which unit you pick.
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Method & sources

How it computes

Area and perimeter for eight shapes — rectangle, circle, triangle (base × height, or Heron in Kahan's stable form), parallelogram, trapezoid, rhombus (perimeter 2√(d₁² + d₂²)), ellipse (perimeter by the complete elliptic integral via the AGM) and regular polygon — converted with exact factors: ft = 0.3048 m, ft² = 0.09290304 m², acre = 43,560 ft² = 4,046.8564224 m² (AreaKernel).

What this tool implements

Exact unit definitions: NIST SP 811 Appendix B.8 (in 0.0254 m, ft 0.3048 m, yd 0.9144 m, ft² 9.290 304 E−02 m², hectare 1.0 E+04 m²); the acre as 43,560 ft² = 4046.856 422 4 m² on the international foot (Federal Register, 5 Oct 2020, Table 1), the U.S. survey foot being deprecated from 1 January 2023 (NIST).
Ellipse perimeter = 4a·E(e) (DLMF 19.9.9), evaluated by the arithmetic-geometric mean (DLMF 19.8) and checked against direct numerical integration of the arc length. The former shortcut 2π√((a² + b²)/2) overstates it by 1.3% at a = 8, b = 5 and by 9.9% at a = 10, b = 1.
Archimedes (287–212 BC), Measurement of a Circle: π between 3 10/71 and 3 1/7 from 96-sided polygons (MacTutor). Heron's formula from his Metrica (MacTutor dates Heron c. 10–75 AD).
Singapore's land area was 581.5 km² in 1965 and 744.3 km² at the end of 2025 (Department of Statistics, table M890151) — about 163 km² added, largely by reclamation.
HDB floor areas on the page are medians of the most recent 5,000 resale transactions of each flat type on data.gov.sg, fetched 19 October 2026: 3-room 67 m², 4-room 93 m², 5-room 117 m².
Corrected 2026-10-19: rounded ft² and acre factors (now exact); the ellipse perimeter (an approximation labelled as the perimeter); the missing rhombus perimeter; grouped input blanked by number fields; unsourced HDB sizes, a "standard practice" tiling allowance, an MOE syllabus timeline and a landmark remark.

Sources

National Institute of Standards and Technology. NIST Guide to the SI (SP 811), Appendix B.8: Factors for units listed alphabetically. https://www.nist.gov/pml/special-publication-811/nist-guide-si-ap…
NIST and NOAA. Deprecation of the United States (U.S.) Survey Foot. Federal Register, 5 October 2020, Table 1. https://www.federalregister.gov/documents/2020/10/05/2020-21902/d…
NIST Digital Library of Mathematical Functions, §19.8 Quadratic Transformations (AGM) and §19.9 (perimeter of an ellipse). https://dlmf.nist.gov/19.9
O'Connor JJ, Robertson EF. Archimedes of Syracuse. MacTutor History of Mathematics, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Archimedes/
O'Connor JJ, Robertson EF. Heron of Alexandria (Metrica). MacTutor History of Mathematics, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Heron/
Singapore Department of Statistics. Land Area (As At December), Annual — table M890151. https://tablebuilder.singstat.gov.sg/table/TS/M890151
Housing & Development Board via data.gov.sg. Resale flat prices based on registration date from Jan-2017 onwards (dataset d_8b84c4ee58e3cfc0ece0d773c8ca6abc), floor_area_sqm. https://data.gov.sg/api/action/datastore_search?resource_id=d_8b8…

What can make this go out of date

None at runtime for the calculation; nothing typed is sent anywhere (the page still pings the tool-status and view endpoints, as before).