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How area calculation works
Area measures the 2-dimensional space a shape occupies, always expressed in square units — in², ft², cm², m², etc. Each geometric shape has a dedicated formula derived from its properties. This calculator applies the exact formula and shows you the full working, so you understand the result — not just the number.
Frequently asked questions
How do you calculate the area of a circle?
Use the formula A = π × r². Square the radius, then multiply by pi (3.14159…). For example, a circle with radius 5 in has an area of π × 25 = 78.54 in².
How do you calculate the area of a rectangle?
Multiply width by height: A = w × h. A rectangle 8 ft wide and 6 ft tall has an area of 48 ft².
How do you calculate the area of a triangle?
Use A = ½ × base × height. The height must be perpendicular to the base. A triangle with base 10 in and height 4 in has an area of 20 in².
How do you calculate the area of a trapezoid?
Add the two parallel sides, multiply by the height, then divide by two: A = ½ × (a + b) × h.
Why is area always in square units?
Area is a two-dimensional measurement — it covers length × length, so the unit gets squared. If your inputs are in inches, your result is in square inches (in²). Never mix units within a single calculation.
Circle area calculator
Use the circle area calculator to find the area of any circle. Formula: A = π × r², where r is the radius. Multiply pi (3.14159) by the radius squared. Example: a circle with radius 7 inches has an area of 153.94 in².
Square area calculator
Use the square area calculator to find the area of any square. Formula: A = s², where s is the length of one side. Multiply the side length by itself. Example: a square with side 9 ft has an area of 81 ft².
Rectangle area calculator
Use the rectangle area calculator to find the area of any rectangle. Formula: A = w × h, where w is the width and h is the height. Multiply width by height. Example: a rectangle 12 cm wide and 5 cm tall has an area of 60 cm².
Triangle area calculator
Use the triangle area calculator to find the area of any triangle. Formula: A = ½ × base × height. The height must be perpendicular to the base. Example: a triangle with base 10 in and height 6 in has an area of 30 in².
Trapezoid area calculator
Use the trapezoid area calculator to find the area of any trapezoid. Formula: A = ½ × (a + b) × h, where a and b are the two parallel sides and h is the height. Example: a trapezoid with parallel sides 8 ft and 5 ft and height 4 ft has an area of 26 ft².
Ellipse area calculator
Use the ellipse area calculator to find the area of any ellipse. Formula: A = π × a × b, where a and b are the two semi-axes. Example: an ellipse with semi-axes 6 cm and 4 cm has an area of 75.40 cm².
Parallelogram area calculator
Use the parallelogram area calculator to find the area of any parallelogram. Formula: A = base × height. The height is the perpendicular distance between the two parallel bases. Example: a parallelogram with base 10 m and height 3 m has an area of 30 m².
Sector area calculator
Use the sector area calculator to find the area of any circle sector. Formula: A = ½ × r² × θ, where r is the radius and θ is the central angle in radians. Enter the angle in degrees and the calculator converts automatically. Example: a sector with radius 5 in and angle 90° has an area of 19.63 in².