Area Calculator
Choose a shape, enter dimensions, and calculate area instantly.
Result will be shown in square units (for example, cm²).
Why area formulas matter
Area tells you how much surface a flat shape covers. Whether you are planning flooring, painting a wall, laying sod in a yard, or solving geometry homework, area formulas help you get accurate measurements quickly. A good understanding of these formulas also improves estimation skills and reduces costly mistakes in real-world projects.
Quick reference: common area formulas
- Square: A = s²
- Rectangle: A = l × w
- Triangle: A = (1/2) × b × h
- Circle: A = πr²
- Parallelogram: A = b × h
- Trapezoid: A = (1/2) × (a + b) × h
- Ellipse: A = πab
- Sector: A = (θ/360) × πr²
Understanding symbols in formulas
Most area formulas use a shared set of symbols. You will typically see:
- A = area
- b = base
- h = height (perpendicular to the base)
- l and w = length and width
- r = radius
- π = approximately 3.14159
- a and b (ellipse/trapezoid contexts) = major dimensions or base lengths
- θ = central angle in degrees (for sectors)
One common confusion: area always uses squared units, such as cm², m², ft², or in². Linear units like cm or m are not enough when reporting area.
Area formulas by shape
1) Square
A square has all sides equal. If one side is s, then:
A = s²
Example: If s = 8 cm, then area = 8² = 64 cm².
2) Rectangle
A rectangle uses length and width:
A = l × w
Example: A room that is 5 m by 4 m has area 20 m².
3) Triangle
The triangle formula is half of a rectangle with the same base and height:
A = (1/2) × b × h
Example: b = 12 m, h = 7 m → A = 0.5 × 12 × 7 = 42 m².
4) Circle
A circle uses radius:
A = πr²
Example: r = 3 in → A ≈ 3.14159 × 9 = 28.27 in².
5) Parallelogram
Similar to a rectangle, but with slanted sides:
A = b × h
Use the perpendicular height, not the slanted side length.
6) Trapezoid
A trapezoid has two parallel sides (bases). The area is the average of bases times height:
A = (1/2) × (a + b) × h
Example: a = 10, b = 6, h = 4 → A = 0.5 × 16 × 4 = 32 square units.
7) Ellipse
For an ellipse, use semi-major axis a and semi-minor axis b:
A = πab
This is useful in astronomy, architecture, and design where circular shapes are stretched.
8) Sector of a circle
A sector is a slice of a circle:
A = (θ/360) × πr²
Example: r = 10 and θ = 90° gives one-quarter of the full circle area.
How to solve area problems correctly
- Identify the shape first.
- Write the correct formula before plugging in numbers.
- Check that dimensions use the same unit system.
- Substitute values carefully and compute.
- Report your result in squared units.
Unit conversion tips
Converting area units is not the same as converting length units. Because area is squared, the conversion factor must be squared too.
- 1 m = 100 cm, so 1 m² = 10,000 cm²
- 1 ft = 12 in, so 1 ft² = 144 in²
- 1 yd = 3 ft, so 1 yd² = 9 ft²
Always convert dimensions before calculation or convert final area using the correct squared factor.
Common mistakes to avoid
- Using diameter instead of radius in the circle formula.
- For triangles and parallelograms, using slanted side length instead of perpendicular height.
- Mixing units (for example, meters and centimeters in the same formula).
- Forgetting to square units in final answers.
- Rounding too early and accumulating error.
Real-world applications
Area calculations appear everywhere: estimating paint, determining carpet size, planning tiles, sizing solar panel layouts, land measurement, and engineering design. If you practice these formulas regularly, you can make faster and more confident decisions in both academics and practical projects.
Final takeaway
Mastering area formulas is less about memorization and more about understanding each shape and its dimensions. Keep a short formula reference, verify your units, and use the calculator above for quick checks. Over time, these calculations become second nature.