Area Calculator
Select Shape
Results
| Calculated Area | — |
|---|---|
| Formula | — |
How to Use This Area Calculator
Flooring quotes, lawn seed bags, and geometry sets all ask for flat area—but each shape uses a different formula, and mixing up height with slant length is an easy way to lose points. Pick a shape tab, enter the dimensions labeled on that form, and press Calculate Area.
- Select a shape tab. Circle, Rectangle, Triangle, Trapezoid, Ellipse, Parallelogram, or Sector—only the active tab's fields are used.
- Enter positive measurements. All lengths must be greater than zero. Sector angle is in degrees, capped at 360°.
- Press Calculate Area. The results table shows the numeric area and the formula string for that shape.
- Review steps below. Each run includes a step-by-step block you can compare to your worksheet.
For full circle dimensions (circumference and diameter too), use the Circle Calculator. For 3D surface totals, open the Surface Area Calculator.
Area Formulas and Practical Applications
Area counts how many unit squares cover a flat region. Each diagram below labels the dimensions the matching tab expects—formulas align with what the JavaScript applies on submit.
Circle area
Round patios, manhole covers, and sprinkler zones all start from a single radius. Measure from the center to the rim; if you only have diameter, divide by two before entering.
A = πr²
A 4 m radius round patio covers about 50.27 m².
Rectangle area
Room floors, garden beds, and sheet goods are rectangles—multiply the two perpendicular edge lengths. Order does not matter: l × w equals w × l.
A = l × w
A 12 ft × 8 ft room is 96 ft² of floor to cover.
Triangle area
Gable ends, sail panels, and roof pitches often form triangles. The height must drop straight down to the base at a right angle—using the slant edge instead of h is the mistake we see most often on homework and takeoffs alike.
A = 0.5 × b × h
Base 8 m with height 5 m gives 20 m²—half of what a 8 × 5 rectangle would be.
Trapezoid area
Think of a trapezoid like a tabletop that is wider on one side than the other—only the two parallel edges count as bases. Average those two lengths, then multiply by the perpendicular gap between them.
A = 0.5 × (a + b) × h
Bases 6 m and 10 m with height 5 m yield 40 m².
Ellipse area
An ellipse is a stretched circle—picture a running track infield or an oval tabletop. Use half of each full axis length from the center, not the full width and height of the bounding box.
A = π × a × b
Semi-axes 7 m and 4 m enclose about 87.96 m².
Parallelogram area
A slanted rectangle still has flat parallel top and bottom—the area depends on how far apart those sides are vertically, not how long the tilted edge looks. Same rule as a triangle: perpendicular height only.
A = b × h
Base 12 ft with height 6 ft covers 72 ft².
Circular sector area
A sector is a pie slice—take the full circle area and keep only the fraction your angle represents. A quarter circle is a 90° sector; a semicircle is 180°.
A = πr² × (θ / 360)
Radius 6 m with 90° gives one quarter of the full disk: about 28.27 m².
Standard Units and Conversion Tables
Length inputs cube into area as square units. Keep one unit system per calculation.
| Length unit | Area unit |
|---|---|
| Meters (m) | Square meters (m²) |
| Feet (ft) | Square feet (ft²) |
| Inches (in) | Square inches (in²) |
| Centimeters (cm) | Square centimeters (cm²) |
For solved triangles with all sides and angles, use the Triangle Calculator. Browse math calculators.
Frequently Asked Questions
How is the area of a circle calculated?
A = πr². Radius must be positive. Diameter is not entered on the circle tab—divide by two first or use the Circle Calculator.
What is the difference between base and height in a triangle?
Height is perpendicular to the chosen base. Slant side length is wrong for this tab—that needs the full Triangle Calculator.
How do you find the area of a trapezoid?
Average the parallel bases, multiply by height: 0.5 × (a + b) × h.
What angle unit does the sector tab use?
Degrees from 0° to 360°. A half disk is 180°; a quarter is 90°.
What unit is the area result in?
Square units matching your length input—ft in, ft² out.
Disclaimer. RapidRatio is informational only—not material takeoff or professional estimating advice. Confirm quantities on site.