Area Calculator
Calculate area for 20 common 2D shapes with formulas, steps, unit conversions, and labeled diagrams.
Background
Students often know the shape but are not sure which formula to use or which measurements matter. This calculator helps by organizing shapes into clear groups, showing the formula before substitution, and drawing a labeled sketch so it is easier to distinguish shapes such as parallelogram vs trapezoid, rhombus vs kite, and sector vs circle.
How to use this calculator
- Choose a shape category, then click the exact shape card.
- Enter the measurements required for that shape.
- Select a unit such as cm, m, in, or ft.
- Click Calculate to get the area, optional perimeter, formula, and labeled sketch.
- Use the quick picks for common homework-style examples.
How this calculator works
- Core shapes: use side, base, height, or diagonal formulas depending on the selected figure.
- Circle-family shapes: use πr² and related fractions, angle-based sectors, or subtraction for annuli.
- Polygon shapes: use either side-based closed formulas or the regular-polygon formula A = ½aP.
- Composite / special shapes: split the figure into simpler parts and add their areas.
- Unit support: inputs are interpreted in your chosen unit, then the final area is shown in squared units such as cm², m², in², or ft².
Formula & Equations Used
Square: A = s²
Rectangle: A = l·w
Triangle: A = ½bh
Right Triangle: A = ½ab
Parallelogram: A = bh
Trapezoid: A = ½(b₁ + b₂)h
Rhombus / Kite: A = ½d₁d₂
Circle: A = πr²
Semicircle: A = ½πr²
Quarter Circle: A = ¼πr²
Sector: A = (θ/360)πr²
Annulus: A = π(R² − r²)
Ellipse: A = πab
Regular Polygon: A = ½aP
Pentagon: A = ¼√(5(5+2√5))s²
Hexagon: A = (3√3/2)s²
Octagon: A = 2(1+√2)s²
Rectangle with semicircle ends: A = lw + πr²
Composite rectangle + triangle: A = lw + ½bh
Example Problems & Step-by-Step Solutions
Example 1 — Rectangle
Find the area of a rectangle with length 8 and width 5.
- Use A = l·w.
- Substitute: A = 8·5.
- Compute: A = 40 square units.
Example 2 — Trapezoid
Find the area of a trapezoid with bases 8 and 12 and height 5.
- Use A = ½(b₁ + b₂)h.
- Substitute: A = ½(8 + 12)·5.
- Simplify: A = ½(20)·5 = 10·5 = 50.
Example 3 — Sector
Find the area of a sector with radius 7 and central angle 60°.
- Use A = (θ/360)πr².
- Substitute: A = (60/360)π(7²).
- Simplify: A = (1/6)·49π = 49π/6.
Example 4 — Rhombus
Find the area of a rhombus with diagonals 10 and 8.
- Use A = ½d₁d₂.
- Substitute: A = ½(10)(8).
- Compute: A = 40 square units.
Frequently Asked Questions
Q: What unit will the area use?
Area is shown in squared units such as cm², m², in², or ft² based on your selected input unit.
Q: Why do some shapes also show perimeter?
For many shapes, perimeter is a useful companion value, so the calculator can show it when the needed dimensions are available.
Q: What is the difference between a parallelogram and a trapezoid here?
A parallelogram uses one base and one perpendicular height. A trapezoid uses two parallel bases and a height.
Q: What is the difference between a rhombus and a kite here?
Both can use the diagonal formula for area, but they are different geometric shapes. The calculator keeps them separate to help students identify the correct figure.
Q: What is the difference between a circle and a sector?
A circle uses the full formula πr². A sector is only a portion of a circle, so it also depends on the central angle.