How to use this area calculator
Select the shape and common length unit, then enter each requested positive dimension. Read the shape-specific hint before measuring: a height is perpendicular, an ellipse uses semi-axes and a rhombus uses full diagonals. Changing shape loads example dimensions; changing the unit keeps the numbers but changes their interpretation. Review the formula and substituted dimensions below the result. For a missing rectangle side or a circle known by circumference or area, use the linked specialist calculator instead of forcing those values into an incompatible field.
How the calculation works
Area measures a two-dimensional region in square units. If dimensions are in meters, the result is in square meters; if they are in feet, it is in square feet. Perimeter is a different quantity measured in length units. The value 40 m² describes a covered region and is not interchangeable with 40 m of boundary. Choose the shape and relevant measurements before multiplying, because two plausible-looking dimensions do not automatically define the required area.
Rectangle area uses two perpendicular adjacent sides: A=ab. Square area is a special case with equal sides: A=a². A hypothetical 8 m by 5 m rectangle gives 40 m², while a square of side 5 m gives 25 m². The dedicated Rectangle Calculator additionally supports perimeter, diagonal and inverse constraints. This page intentionally keeps those tasks separate while allowing a rectangular area to be compared with other common plane shapes in one interface.
Triangle area is half a chosen base times its perpendicular height: A=bh/2. For base 8 cm and height 5 cm, area is 20 cm². Height is measured at a right angle to the base line, not along a sloping edge. Some triangles have an altitude whose foot lies outside the base segment; the same perpendicular-height relationship still applies. This interface does not infer that altitude from three sides or from an angle measurement.
Parallelogram area uses the full base-height product, A=bh. With base 8 cm and perpendicular height 5 cm, it gives 40 cm² rather than the triangle's 20 cm². A trapezoid with parallel bases a and b uses their average times perpendicular height: A=(a+b)h/2. Bases 6 m and 10 m with height 4 m give 32 m². Do not substitute one of the nonparallel sides for the separation between the bases.
Circle area is πr² and requires radius, half the diameter. A radius of 5 cm gives about 78.5398 cm². Ellipse area is πab, where a and b are semi-axis lengths measured from the center to the boundary. Semi-axes 6 cm and 4 cm give 24π cm², about 75.3982 cm². Entering the ellipse's full width and full height would multiply the correct area by four, so the diagram and input labels explicitly identify the semi-axis convention.
A rhombus can be calculated from its two full perpendicular diagonals with A=pq/2. Diagonals 8 cm and 6 cm give 24 cm². These are not its side lengths or distances from the center to a vertex. The diagonals divide the shape into four right triangles, which explains the half-product relationship. The tool accepts a rhombus model supplied by the user; it does not verify that a measured four-sided object has equal sides or perpendicular diagonals.
The eight shapes cover common elementary regions, not every polygon or compound floor plan. For a composite outline, divide it into justified nonoverlapping pieces and combine their areas separately, taking care not to count an overlap twice. This calculator has no drawing import, coordinate-polygon editor, cutout subtraction or automatic waste allowance. A result for an ideal shape does not include tile cuts, seams, packaging, land-survey conventions or the irregularities of a physical surface.
All dimensions must use a consistent unit before calculation. The selector relabels the entered numbers rather than converting them. For example, 100 cm and 2 m must first become either 1 m and 2 m or 100 cm and 200 cm before a rectangular area is calculated. Use Area Converter when an area is already known and only its unit needs to change. Using the length conversion factor directly on an area instead of squaring it would give an incorrect conversion.
Positive dimensions from 1e-9 through 1e12 are supported in the chosen length unit, with no zero-width or negative-area geometry. Calculations use double precision and Math.PI where appropriate, retaining intermediate precision before display. This mathematical range does not imply practical measuring accuracy. Check real dimensions, perpendicularity and the chosen shape independently before using the number in purchasing or construction estimates; the result does not certify compliance, material requirements or a safety-critical installation.
Formulas
Straight-sided shapes
Other quadrilaterals
Curved shapes
Worked examples
Triangle and parallelogram on the same base-height inputs
Base 8 cm and perpendicular height 5 cm give triangle area 20 cm² and parallelogram area 40 cm². The shape model determines whether the half factor applies.
Trapezoid with two parallel bases
For parallel bases 6 m and 10 m, with perpendicular height 4 m, A=(6+10)×4/2=32 m². The sloping sides are not needed for this area equation.
Common uses
Compare elementary regions
Use the same unit and a correctly selected shape to compare two-dimensional coverage. A triangle and parallelogram sharing a base and height deliberately produce different areas.
Audit dimensions in a worksheet
Check that a height is perpendicular, an ellipse dimension is a semi-axis and a rhombus input is a full diagonal. Retain those definitions rather than copying two unlabeled lengths.
Prepare a geometric estimate
Find an ideal region's area before separately considering material cuts, overlaps, costs or purchasing allowances. This result is not a complete construction or land-survey assessment.
Accuracy and limitations
Each selected model uses its displayed formula with positive dimensions and double precision. Results are in square units; the tool does not convert preexisting areas or apply waste factors.
Schematic diagrams identify dimensions but are not scaled measurement drawings. Mixed units, unsuitable shape assumptions and inaccurate perpendicular measurements remain source-data problems, not properties the calculator can infer.
Sources and methodology
These primary references explain the numerical methods and units used here. Review the calculation assumptions and limitations alongside the result.
Frequently asked questions
Does this replace Area Converter?
No. This tool calculates area from dimensions. Area Converter changes the unit of an area you already know.
Is the triangle height a sloping side?
No. Use the perpendicular distance to the chosen base line. The tool does not derive height from three sides or angles.
Does ellipse mode take full axes?
No. It uses two semi-axes, each measured from center to edge. Divide full axis lengths by two first.
Can I enter mixed units?
Convert them to one common length unit first. All fields use the selected unit, which is a label rather than an automatic conversion.
Is trapezoid the same shape as a UK trapezium?
The supported shape has two parallel bases and a perpendicular separation. Terminology varies, so follow that definition and diagram.
Does it add a waste percentage?
No. It reports ideal geometric area without extra materials, cuts, overlaps or purchasing allowances.