📐 Area Conversion Calculator
Convert between acres, hectares, m², ft², km² and 50+ area units — with geometry formulas, worked examples & real-world reference guide
🔄 Area Unit Converter
📊 All Conversions at Once
📖 How to Use the Area Converter
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1Enter Your Area Value
Type the numerical area value in the "Enter Value" field. Decimals and large numbers are supported (e.g., 43560 for one acre in square feet). Results update live as you type.
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2Filter by Category (Optional)
Click a category button — Metric, Imperial/US, Land/Survey, or Historic & Regional — to narrow the dropdown lists. Select "All Units" to see all 50+ units at once.
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3Select the Source Unit (From)
Choose your input unit from the "From Unit" dropdown — from square millimeter (mm²) to township, including international units such as bigha, tsubo, rai and dunam.
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4Select the Target Unit (To)
Choose the unit you want to convert into from the "To Unit" dropdown. The result and the exact multiplication factor appear immediately in the blue result panel.
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5Use Quick-Convert Buttons & Copy
Click a quick-convert button (Acre→m², ft²→m², ha→Acre, etc.) for the most common conversions. The "All Conversions" panel shows your value in every supported unit simultaneously. Click "📋 Copy Result" to copy to clipboard.
📐 Area Units Reference Table
| Unit | Symbol | Value in m² | Math Expression | Common Use |
|---|---|---|---|---|
| Square Meter | m² | \(1\,\text{m}^2\) | \( 1\,\text{m}^2 = 1\,\text{m} \times 1\,\text{m} \) | SI base unit, rooms, plots |
| Square Kilometer | km² | \(10^6\,\text{m}^2\) | \( 1\,\text{km}^2 = (10^3)^2 = 10^6\,\text{m}^2 \) | Countries, large regions |
| Hectare | ha | \(10{,}000\,\text{m}^2\) | \( 1\,\text{ha} = 10^4\,\text{m}^2 \) | Agriculture, land worldwide |
| Are | a | \(100\,\text{m}^2\) | \( 1\,\text{are} = 10^2\,\text{m}^2 \) | European land surveys |
| Acre | ac | \(4{,}046.8564\,\text{m}^2\) | \( 1\,\text{ac} = 43{,}560\,\text{ft}^2 \) | US/UK land & real estate |
| Square Foot | ft² | \(0.0929\,\text{m}^2\) | \( 1\,\text{ft}^2 = (0.3048)^2\,\text{m}^2 \) | Real estate, architecture |
| Square Yard | yd² | \(0.8361\,\text{m}^2\) | \( 1\,\text{yd}^2 = (0.9144)^2\,\text{m}^2 \) | Flooring, fabric |
| Square Mile | mi² | \(2{,}589{,}988\,\text{m}^2\) | \( 1\,\text{mi}^2 = (1609.344)^2\,\text{m}^2 \) | Geographic regions |
| Square Inch | in² | \(6.452 \times 10^{-4}\,\text{m}^2\) | \( 1\,\text{in}^2 = (0.0254)^2\,\text{m}^2 \) | Engineering, printing |
| Square Centimeter | cm² | \(10^{-4}\,\text{m}^2\) | \( 1\,\text{cm}^2 = (10^{-2})^2\,\text{m}^2 \) | Small surfaces, lab work |
📏 Understanding Area — A Complete Guide
Area is a fundamental physical quantity that measures the extent of a two-dimensional surface or plane figure. It is one of the oldest mathematical concepts — ancient Egyptian surveyors used area calculations more than 4,000 years ago to re-establish farmland boundaries after Nile floods erased property markers. Today, area measurement spans every scale imaginable: from the cross-section of a transistor gate measured in nanometres squared, to the surface area of Earth's landmass measured in square kilometres, all the way to the area of the observable universe.
The SI (International System of Units) base unit of area is the square meter (m²), defined as the area of a square with sides exactly one meter long. All other area units can be expressed mathematically as exact or approximate multiples of the square meter. Whether you are a real-estate agent converting square feet to square meters, a farmer comparing acreage to hectares, a geographer working with square miles, or a scientist calculating nuclear cross-sections in barns, a reliable area converter is an indispensable daily tool.
This deceptively simple formula is the foundation of all area measurement. For non-rectangular shapes — circles, triangles, trapezoids, irregular polygons — different geometric formulas apply, but ultimately every area calculation reduces to counting how many unit squares (square meters, square feet, etc.) fit within the boundary of a shape. The unit conversion challenge then becomes: how many of unit B fit inside one unit A? Our calculator answers this instantly for 50+ unit pairs.
📐 Essential Area Geometry Formulas
Before converting between unit systems, you often need to calculate an area from length measurements. The following formulas, all rendered in standard mathematical notation, cover the most common geometric shapes encountered in everyday applications — from home improvement to civil engineering.
Given: A circular garden with diameter = 14 m, so radius \( r = 7 \) m.
\[ A = \pi r^2 = \pi \times 7^2 = \pi \times 49 \approx 153.94\,\text{m}^2 \]
\[ 153.94\,\text{m}^2 \approx 0.038\,\text{acres} \approx 0.01539\,\text{hectares} \approx 1{,}657.6\,\text{ft}^2 \]
Answer: The garden covers approximately 154 m², or just under 0.04 acres — use the converter above to check any unit instantly.
🔢 Metric Area Units — The SI Scale
The metric system organizes area units as a factor-of-100 ladder because area is a two-dimensional quantity — each step up in the length prefix (×10) corresponds to a step of ×100 in area. Understanding this hierarchy is essential for rapid mental conversions:
Square Millimeter (mm²) — \(10^{-6}\,\text{m}^2\)
Smallest commonly used metric unit. Applied in material science, micro-electronics, cross-sections of wires and metals. 1 mm² = 0.01 cm² = 0.00155 in².
Square Centimeter (cm²) — \(10^{-4}\,\text{m}^2\)
Used in medicine, biology, and cooking. Blood pressure is measured per cm² (mmHg). A standard postage stamp is about 10 cm². 1 cm² = 100 mm² = 0.155 in².
Square Meter (m²) — SI Base
Universal unit for room sizes, apartment listings, and construction. A standard car parking space is about 12.5 m². Average US apartment: ~90 m². 1 m² = 10.764 ft².
Hectare (ha) — \(10^4\,\text{m}^2\)
The primary unit for agricultural land worldwide. 1 ha = 10,000 m² = 2.471 acres. An international football pitch (105 m × 68 m) ≈ 0.714 ha. About 2.5 American football fields.
Square Kilometer (km²) — \(10^6\,\text{m}^2\)
Used for countries, states, and geographic regions. Singapore ≈ 733 km². New York City ≈ 783 km². 1 km² = 100 ha = 0.3861 mi².
🏡 Imperial & US Area Units
The United States, United Kingdom, and several other countries use imperial area units for everyday measurements — particularly in real estate, agriculture, and land surveying. The following conversion formulas relate imperial units to the square meter with full mathematical precision.
Square Foot (ft²)
Dominant unit in US/Canada/UK real estate. The average American home is about 2,000 ft² (186 m²). 1 ft² = 144 in² = 0.0929 m². To convert: \( \text{m}^2 = \text{ft}^2 \times 0.0929 \).
Acre
The most important land unit in the US and UK. Originally the area one yoke of oxen could plough in a day. 1 acre = 43,560 ft² = 4,047 m² ≈ 0.405 ha. A typical American football field ≈ 1.32 acres.
Square Yard (yd²)
Used for flooring, carpets, and fabric. 1 yd² = 9 ft² = 0.8361 m². A standard door is about 2 yd². Common in UK/Ireland for small garden areas.
Square Mile (mi²)
US geographic unit for states and counties. 1 mi² = 640 acres = 2.59 km². Rhode Island ≈ 1,545 mi². A township (US survey) = 36 mi² = 36 sections.
Problem: A US listing says a plot is 0.75 acres. What is that in square feet, square meters, and hectares?
\[ 0.75\,\text{acres} \times 43{,}560\,\frac{\text{ft}^2}{\text{acre}} = 32{,}670\,\text{ft}^2 \]
\[ 0.75\,\text{acres} \times 4{,}046.8564\,\frac{\text{m}^2}{\text{acre}} \approx 3{,}035.1\,\text{m}^2 \]
\[ \frac{3{,}035.1\,\text{m}^2}{10{,}000} = 0.30351\,\text{ha} \]
Answer: 0.75 acres = 32,670 ft² = 3,035 m² = 0.304 ha.
📋 Land & Survey Units Explained
The US Public Land Survey System (PLSS) and traditional British surveying introduced several specialized area units that remain in official land records and legal documents. Understanding these units is essential for anyone working with historic deeds, land titles, or agricultural records.
| Unit | In m² | Relation | Context |
|---|---|---|---|
| Section | \(2{,}589{,}988\,\text{m}^2\) | \(1\,\text{section} = 1\,\text{mi}^2 = 640\,\text{acres}\) | US PLSS base unit |
| Township | \(93{,}239{,}572\,\text{m}^2\) | \(1\,\text{township} = 36\,\text{sections}\) | US PLSS super-unit |
| Homestead | \(647{,}497\,\text{m}^2\) | \(1\,\text{homestead} = \frac{1}{4}\,\text{section} = 160\,\text{acres}\) | US Homestead Act grants |
| Rood | \(1{,}011.7\,\text{m}^2\) | \(1\,\text{rood} = \frac{1}{4}\,\text{acre} = 10{,}890\,\text{ft}^2\) | Historic English land |
| Square Rod / Perch | \(25.293\,\text{m}^2\) | \(1\,\text{sq rod} = 30\frac{1}{4}\,\text{yd}^2\) | Garden, allotment sizing |
| Square Chain | \(404.686\,\text{m}^2\) | \(1\,\text{sq chain} = \frac{1}{10}\,\text{acre}\) | Gunter's chain surveys |
| Acre [Survey] | \(4{,}046.873\,\text{m}^2\) | \(\approx 0.0016\%\) larger than international acre | US geodetic surveys |
🌍 Global & Historic Area Units
Land area has been measured differently across cultures for millennia. Each civilization developed units suited to their local context — the land a team of oxen could plough in a morning, the area of a standardised mat, or the traditional village allotment size. While the metric system is now the international standard, these traditional units remain legally relevant in many countries and are still encountered in property records, agricultural leases, and cultural references.
| Unit | Region | In m² | Notes |
|---|---|---|---|
| Bigha | India | \(\approx 2{,}508\,\text{m}^2\) | Varies by state; 1 bigha ≈ 0.6 acres (Uttar Pradesh) |
| Kattha | Nepal/Bangladesh | \(\approx 338.6\,\text{m}^2\) | 1 bigha = 20 kattha (Nepal) |
| Dunam / Donum | Middle East | \(1{,}000\,\text{m}^2\) | = 0.1 ha; used in Turkey, Israel, Jordan, Iraq |
| Jerib | Iran/Afghanistan | \(2{,}000\,\text{m}^2\) | = 2 dunam; varies regionally |
| Rai | Thailand | \(1{,}600\,\text{m}^2\) | 1 rai = 4 ngan = 400 square wah |
| Tsubo | Japan | \(3.3058\,\text{m}^2\) | = 2 tatami; used in Japanese real estate |
| Tatami | Japan | \(1.6529\,\text{m}^2\) | Traditional floor mat; rooms sized in tatami count |
| Morgen | Germany | \(2{,}500\,\text{m}^2\) | "Morning" = area ploughable in one morning |
| Morgen | South Africa | \(8{,}565\,\text{m}^2\) | Still used in Cape wine-farm measurements |
| Stremma | Greece | \(1{,}000\,\text{m}^2\) | = 1 dunam; metric stremma standardised 1910 |
| Cuerda | Puerto Rico | \(3{,}930\,\text{m}^2\) | Spanish colonial unit; still used legally in PR |
| Oxgang / Bovate | Medieval England | \(\approx 60{,}703\,\text{m}^2\) | Area one ox could plough per year ≈ 15 acres |
| Hide / Carucate | Medieval England | \(\approx 485{,}623\,\text{m}^2\) | ≈ 120 acres; Domesday Book taxation unit |
| Barn | Physics | \(10^{-28}\,\text{m}^2\) | Nuclear cross-section unit: \(1\,\text{b} = 10^{-28}\,\text{m}^2\) |
🔁 Area Unit Conversion — The Mathematics
All unit conversions in our calculator use the square meter as the universal pivot. Each unit stores a factor \(f\) representing its value in square meters. The conversion from unit A to unit B follows:
Convert 5 acres to hectares.
Step 1 — Factor for acre: \( f_{\text{acre}} = 4{,}046.8564\,\text{m}^2 \)
Step 2 — Factor for hectare: \( f_{\text{ha}} = 10{,}000\,\text{m}^2 \)
Step 3 — Apply formula: \[ A_{\text{ha}} = 5 \times \frac{4{,}046.8564}{10{,}000} = 5 \times 0.40468564 = 2.0234\,\text{ha} \]
Answer: 5 acres = 2.0234 hectares (≈ 2 ha — a useful number to remember!)
Convert 100 km² to square miles.
\[ f_{\text{km}^2} = 1{,}000{,}000\,\text{m}^2 \qquad f_{\text{mi}^2} = 2{,}589{,}988.1\,\text{m}^2 \]
\[ A_{\text{mi}^2} = 100 \times \frac{10^6}{2{,}589{,}988.1} = 100 \times 0.38610 = 38.610\,\text{mi}^2 \]
Answer: 100 km² ≈ 38.61 mi². Quick approximation: divide km² by 2.59 to get mi².
🌐 Real-World Area Reference Points
Area units become far more intuitive when anchored to familiar real-world objects. The following reference points help you instantly gauge whether a quoted area is reasonable — invaluable when evaluating property listings, comparing countries, or designing spaces.
| Reference | Approximate Area | In Multiple Units |
|---|---|---|
| Credit card | \(46\,\text{cm}^2\) | 7.13 in² | 0.00046 m² |
| A4 paper sheet | \(623\,\text{cm}^2\) | 0.0623 m² | 0.671 ft² |
| Car parking space | \(12.5\,\text{m}^2\) | 134.5 ft² | 14.95 yd² |
| Tennis court | \(260.8\,\text{m}^2\) | 2,808 ft² | 0.064 acres |
| American football field | \(5{,}351\,\text{m}^2\) | 57,600 ft² | 1.32 acres |
| 1 city block (US avg.) | \(\approx 80{,}937\,\text{m}^2\) | 20 acres | 8.09 ha |
| Central Park, NYC | \(3.41\,\text{km}^2\) | 341 ha | 843 acres |
| Manhattan Island | \(59.1\,\text{km}^2\) | 5{,}910 ha | 14{,}601 acres |
| Rhode Island (US state) | \(4{,}001\,\text{km}^2\) | 1,545 mi² | 988,717 acres |
| Russia (largest country) | \(17{,}098{,}246\,\text{km}^2\) | 6.6 million mi² | 1.71 billion ha |