Use this area calculator to find the area of common 2D shapes, convert units, and check whether your measurements make sense.
How to use our Area Calculator
- Choose a value in Shape for the figure you want to measure.
- If you picked Triangle, choose the correct Triangle method: base and height, three sides, or two sides and included angle.
- Select the Length unit that matches every length you will enter, such as feet or meters.
- Select Area result unit for how you want the final answer displayed, such as square feet, square meters, acres, or hectares.
- Enter the needed values in Primary measure 1, Primary measure 2, and, when required, Primary measure 3. The meaning of each field changes with the shape, so check the label help if you are unsure.
- Choose Decimal places to control rounding in the displayed results.
- Click Calculate to see Area, Area in square base unit, Formula used, and Input check.
- Sanity-check the result: if Area in square base unit looks reasonable for your lengths and Input check says the shape is valid, your answer is more likely correct.
Definitions
Shape: The 2D figure you want to measure, such as a rectangle, circle, or trapezoid.
Triangle method: The set of triangle measurements you know: base and height, three sides, or two sides with the included angle.
Length unit: The unit used for all entered lengths, such as inches, feet, centimeters, or meters.
Area result unit: The unit used for the final area, such as square feet, square meters, acres, or hectares.
Area: The amount of flat surface inside a shape.
Area in square base unit: The same area shown in the square version of your chosen Length unit, like square feet if your lengths were entered in feet.
Included angle: The angle formed between the two sides you entered in triangle SAS mode.
Perpendicular height: A height that meets the base at a right angle, not a slanted edge.
Semi-major axis and semi-minor axis: For an ellipse, these are the half-lengths of the long axis and short axis.
Common mistakes and quick fixes
Mistake: Entering a diameter in Primary measure 1 for a circle when the formula expects a radius.
Fix: For Shape = Circle, enter half the full width as Primary measure 1 and then recalculate Area .
Mistake: Using a slanted side instead of a perpendicular height for a triangle, trapezoid, or parallelogram.
Fix: When Shape is Triangle with base-height, Trapezoid, or Parallelogram, make sure Primary measure 2 or Primary measure 3 is the straight up-and-down height, not the tilted side.
Mistake: Mixing feet, inches, or meters in the same problem while only one Length unit is selected.
Fix: Convert all lengths to one unit first, then enter them with the matching Length unit so Area in square base unit is correct.
Mistake: Choosing the wrong Triangle method for the measurements you know.
Fix: If you know base and perpendicular height, use base-height. If you know all three sides, use three sides. If you know two sides and the included angle, use SAS before checking Formula used .
Mistake: Entering side lengths in Primary measure 1 , Primary measure 2 , and Primary measure 3 that cannot make a real triangle.
Fix: In Triangle three-sides mode, each side must be less than the sum of the other two. If not, Input check will show an error and the result should be fixed.
Mistake: Thinking a very small number in Area means the calculator is wrong when Area result unit is acres or hectares.
Fix: Small shapes often become tiny decimal values in land units. Compare with Area in square base unit to confirm the conversion.
Limitations & Key Assumptions / Boundary Conditions
- The calculator only handles the listed 2D shapes: rectangle, square, triangle, circle, trapezoid, parallelogram, ellipse, and sector.
- All length entries must use the same Length unit. It does not mix units inside one calculation.
- For triangle base-height, trapezoid, and parallelogram, the height must be perpendicular to the base. Using a slanted side gives the wrong area.
- For triangle three-sides mode, the three side lengths must satisfy the triangle inequality or no real triangle exists.
- For triangle SAS mode, the included angle must be greater than 0 degrees and less than 180 degrees.
- For sector mode, the central angle must be greater than 0 degrees and no more than 360 degrees.
- Ellipse inputs are semi-axis lengths, not full width and full height.
- Results are rounded for display based on Decimal places, so the shown value may differ slightly from the full internal value.
- Very small areas shown in acres or hectares can look tiny but still be correct because those are large land-area units.
Methodology
How the calculator finds area
The calculator first computes area in the square of the chosen Length unit. After that, it converts the result into the selected Area result unit. This helps keep the shape formula separate from the unit conversion.
Shape formulas used
Rectangle: A = l * w
Square: A = s^2
Triangle, base-height: A = (b * h) / 2
Triangle, three sides: s = (a + b + c) / 2
Triangle, three sides: A = sqrt(s * (s - a) * (s - b) * (s - c))
Triangle, SAS: A = (a * b * sin(C)) / 2
Circle: A = pi * r^2
Trapezoid: A = ((b1 + b2) / 2) * h
Parallelogram: A = b * h
Ellipse: A = pi * a * b
Sector: A = (theta / 360) * pi * r^2
Unit conversion method
After finding the base area, the calculator converts length units to meters, squares that scale factor, and then converts square meters to the requested area unit.
A_out = A_base * (m_per_len^2) / (m2_per_out_unit)
Examples of exact conversion constants used are 1 foot = 0.3048 m, 1 inch = 0.0254 m, 1 yard = 0.9144 m, 1 acre = 4046.8564224 m^2, and 1 hectare = 10000 m^2.
Worked mini-example
Suppose Shape is Rectangle, Length unit is feet, and the two side lengths are 12 and 8. The base area is 12 * 8 = 96 square feet.
A_base = 12 * 8 = 96 sq ft
If Area result unit is also square feet, no further scale change is needed, so Area = 96 square feet.
A_out = 96 sq ft
As another example, for a 3 meter radius circle, the calculator uses pi * 3^2, giving about 28.2743 square meters before display rounding [1].
A = pi * 3^2 = 28.2743...
Validity checks
The calculator blocks blank or non-numeric required inputs for the active shape. It also requires positive lengths, checks triangle inequality in three-sides mode, requires an included angle strictly between 0 and 180 degrees in SAS mode, and requires a sector angle greater than 0 and at most 360 degrees. Heron's formula is used only when the three side lengths can form a real triangle [2].
Output interpretation
Area is the main answer in your chosen output unit. Area in square base unit is the same quantity in the square version of your chosen length unit, which is useful for checking whether your unit choices make sense. Formula used tells you which geometry rule matched the active shape and triangle method. Input check reports whether the measurements form a valid shape.
Assumptions behind the result
The result assumes ideal flat geometric shapes, exact measurements, and degree-based angles for sector and triangle SAS mode. Real objects may differ slightly because of measurement error, rounding, or because the shape is only an approximation of the real object.