Area Calculator
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.
Area Calculator Tool
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 automatically. This is especially useful for HDB flat measurements, land area comparisons, and property calculations where different units are common.
Area — The Foundation of Geometry, Architecture and Real Estate
Area Formulas From PSLE to O-Level
Area is the measurement of a two-dimensional surface — the amount of space enclosed within a boundary. In Singapore's MOE mathematics curriculum, area formulas appear from Primary 4 onwards, building from rectangles and squares through to circles and composite figures at the Primary School Leaving Examination (PSLE) level. By O-Level Additional Mathematics, students are expected to derive area formulas from first principles and apply integration to irregular shapes.
One of the most common mistakes in school examinations is confusing area with perimeter. Area measures the surface enclosed (in square units); perimeter measures the boundary length (in linear units). A rectangle that is 10 cm by 5 cm has an area of 50 cm² and a perimeter of 30 cm — two entirely different quantities answering different questions. This calculator shows both, precisely to prevent that confusion.
The formula for the area of a circle — A = πr² — was famously derived by Archimedes of Syracuse (287–212 BC) using his method of exhaustion. By inscribing and circumscribing regular polygons with increasing numbers of sides around a circle, he squeezed the true area between two converging bounds, arriving at an approximation of π that was accurate to within 0.04%. More than 2,200 years later, the same formula is still tested at every level of mathematics education worldwide.
Real-World Area: HDB Renovation in Singapore
Singapore's Housing Development Board (HDB) flats are measured and marketed in square metres, but many Singaporeans ask "how many square feet?" when evaluating a flat. The conversion is: 1 m² = 10.764 sq ft. As a practical guide: a 2-room flexi flat is approximately 40 m² (431 sq ft); a 3-room flat is around 65 m² (700 sq ft); a 4-room flat is 90 m² (968 sq ft); a 5-room flat is 110 m² (1,184 sq ft). Property agents in Singapore commonly quote prices per square foot (psf) when comparing market value.
"Singapore HDB flats are measured in square metres, but many ask 'how many square feet?' — a 4-room HDB flat is approximately 900-970 sq ft or 83-90 m²."
For HDB renovation projects, area calculation is critical. When purchasing flooring tiles or timber, contractors advise buying 10–15% extra beyond the measured floor area to account for cutting waste, pattern matching, and future replacements. For a 4-room flat with 90 m² of floor space, a renovator should order approximately 99–103 m² of tiles. The Area Calculator helps homeowners plan accurately: measure each room (rectangle inputs), sum the areas, then add the waste buffer. For oddly shaped rooms or bay windows, the trapezoid or parallelogram shapes may give a closer estimate.
Singapore property agents list condominiums in both sq ft and m². Local buyers often need to convert between the two — this calculator's automatic unit conversion row (m², ft², acres) makes that instant. Land in Singapore is increasingly precious: the island spans approximately 733 km² of total area, expanded from 580 km² at independence through over 150 km² of land reclamation — itself a massive geometry problem solved one hectare at a time.
Why π Never Ends — And Why That Matters for Area
The number π (pi) appears in the area formula for every curved shape — circles, ellipses, and regular polygons with large numbers of sides (which approach a circle). π is irrational and transcendental: its decimal expansion never repeats and never terminates. Archimedes proved it lies between 3 10/71 and 3 1/7 (approximately 3.1408 to 3.1429). The value 22/7, still used in many school curricula, gives 3.142857... — accurate to 0.04%.
The intuition behind the circle area formula is elegant: imagine cutting a circle into infinitely many thin pie-slice triangles, then rearranging them into a rectangle. The base of the rectangle is half the circumference (πr) and the height is the radius (r), giving area = πr × r = πr². This same idea — approximating curved areas with straight-sided triangles — underpins integral calculus. A pizza with a 30 cm diameter has four times the area of a 15 cm pizza, not twice — a fact that regularly surprises diners comparing "large" and "small" options. The circular auditorium spaces in Marina Bay Sands and the Singapore Flyer's gondola shape are all calculated with exactly this formula.
10 Facts About Area and Geometry
Archimedes (287–212 BC) derived the circle area formula using his method of exhaustion — the forerunner of integral calculus — over 1,900 years before Newton.
Singapore's total land area is approximately 733 km² — roughly 1.3 times the size of New York City's five boroughs combined.
A typical 4-room HDB flat in Singapore is about 90 m² (968 sq ft) — knowing this helps you calculate flooring, paint, and tile quantities instantly.
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. 10–70 AD) devised his triangle area formula from three sides alone — it is still taught at O-Level mathematics in Singapore today.
Singapore has reclaimed over 150 km² of land from the sea since independence — making it one of the world's most ambitious land-area expansion projects.
A circle always encloses more area than a square with the same perimeter — for a 28 cm perimeter, a circle gives 62.1 cm² versus 49 cm² for a square.
The New Century Global Center in Chengdu, China, covers 1.76 million m² of floor area — the largest single building by floor area in the world.
The Petronas Towers in Kuala Lumpur are built on an 88-sided regular polygon footprint — a nod to Islamic geometric design principles.
1 acre = 4,047 m² — roughly the size of a standard American football field (without end zones), or about 45 standard HDB 4-room flats.
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 was derived by Heron of Alexandria around 60 AD and is covered in Singapore's O-Level Additional Mathematics syllabus.
-
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.
-
Multiply by 10.764. So 90 m² × 10.764 = 968.7 sq ft. To go the other way (sq ft to m²), divide by 10.764, or multiply by 0.0929. 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 10–15% extra for cutting waste: multiply total area × 1.12 for a 12% buffer. This is standard practice for Singapore HDB renovation tiling and laminate flooring projects.
-
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 (Singapore) or ft (US/Malaysia property listings). The unit conversion row shows your result in m², ft² and acres regardless of which unit you pick.
-
100% free, forever. No account, no subscription, no hidden limits. RECATOOLS is funded by contextual advertising, not paywalls. The tool works with or without ad consent enabled and requires no data connection — all calculations happen locally in your browser.
Related News
You may be interested in these recent stories from our newsroom.
No related news yet for this tool. Our editorial team publishes new pieces every week.
Browse all news →75 more free tools
Calculators, converters, security tools — no signup.