Square Feet of a Triangle Calculator
Find a triangle's area in square feet from base and height, three sides, side-angle-side, or angle-side-angle measurements.
Triangle measurements
Live results
Triangle area is 48 square feet.
Calculation details
| Quantity | Value | Unit or meaning |
|---|---|---|
| Base | 12 | ft |
| Perpendicular height | 8 | ft |
| Base × height | 96 | ft² |
| Triangle area | 48 | ft² |
How to use the square feet of a triangle calculator
What this calculator does
This calculator finds the area of a plane triangle and reports the main answer in square feet. It supports four standard measurement sets: base and perpendicular height, three sides, two sides with their included angle, and two angles with the side between them. It also converts the result to the square of the selected length unit, square yards, and square meters. The result is a mathematical area estimate based on the measurements supplied; it does not add waste allowances, material thickness, slope corrections, or project-specific coverage factors.
When to use it
Use it to estimate triangular floor or wall sections, roof-gable faces, landscape beds, fabric or sheet material, classroom geometry exercises, and survey sketches. It is especially useful when the triangle is not right-angled and you know either all three sides or a combination of sides and angles.
How to calculate
- The calculator opens with a ready-to-use example: a 12 ft base and an 8 ft perpendicular height. The first result is 48 ft², and the example Excel workbook is immediately available.
- Choose a measurement pattern in Known triangle details. Only the fields needed for that pattern remain visible.
- Select the common Length unit. When you change the unit, the calculator converts every entered length rather than merely relabeling it.
- Replace the sample measurements with positive decimal values using a period as the decimal separator. Commas are accepted only as standard three-digit grouping marks, such as 1,250.5.
- Read Area in square feet first, then review the converted results, formula, and calculation table. Select Download Excel for a current-state workbook.
- Select Reset to clear all demonstration and entered measurements. Reset leaves the method at base and height and the unit at feet, but it removes the numbers and may disable Download Excel until a complete valid set is entered again.
Input guide
Known triangle details is required and selects the formula. Base and height expects Base and Perpendicular height, both positive lengths; the height must meet the chosen base at 90 degrees. A realistic pair is 12 ft and 8 ft. Increasing either value increases area proportionally. A slanted side is not a perpendicular height.
Three sides (SSS) requires positive Side a, Side b, and Side c. The sample 6, 6, 6 forms an equilateral triangle. Any two sides must add to more than the third; 2, 3, and 5 is degenerate and is rejected. The calculator applies Heron's formula, which is explained in the OpenStax treatment of non-right triangles and Heron's formula.
Side-angle-side (SAS) requires positive SAS side a and SAS side b, plus the Included angle between them. The angle is entered in degrees and must be greater than 0° and less than 180°; 10 ft, 8 ft, and 45° is a practical example. A common mistake is entering an angle that is not between the two stated sides.
Angle-side-angle (ASA) requires the positive ASA included side a, Angle β, and Angle γ. Each angle must be between 0° and 180°, and their sum must be less than 180° so the third angle remains positive. The sample values are 12 ft, 55°, and 65°. Length unit applies to every length field; supported choices are feet, inches, yards, meters, and centimeters. Angle fields always remain in degrees.
Output guide
The summary pills show Method, Unit, and Status. Status is ready for a finite valid model, waiting after Reset, and needs attention when an active field is invalid. Area in square feet is the primary converted area. Area in selected unit² reports the area in the square of the chosen length unit. Area in square yards and Area in square meters are unit conversions of the same area; NIST explains that area is measured in square units in its SI units guide for area. Zero is not a valid triangle area here because all supported measurement sets require a nondegenerate triangle.
Formula used identifies the governing identity. The Calculation details table has three columns: Quantity names each input or intermediate, Value gives its current numeric amount, and Unit or meaning distinguishes lengths, areas, angles, and dimensionless factors. These outputs are exact identities for the entered measurements apart from display rounding and measurement uncertainty in the source data.
Worked example
With the startup values Base = 12 ft and Perpendicular height = 8 ft, the base-height formula is A = ½ × b × h. Substituting the values gives A = ½ × 12 × 8 = 48 ft². The same area is 5.3333 yd² and approximately 4.4593 m². Those values appear in the first rendered results, calculation table, and initial workbook.
How the four triangle formulas work
Base and height uses half the area of a parallelogram:
For three known sides, let s = (a + b + c) / 2. Heron's formula is:
The independent MathWorld reference for Heron's formula gives the same semiperimeter relationship. For SAS, the area is half the product of the two sides and the sine of their included angle: A = ½ab sin(γ). For ASA, where side a lies between β and γ, the formula is A = a² sin(β) sin(γ) / [2 sin(β + γ)].
Measurement and interpretation notes
Keep all source lengths in the same unit before interpreting the geometry. The calculator's unit selector performs exact length conversion using the international foot relationship and squares the factor for area. Rounding should happen only after the area calculation, particularly when dimensions will feed a cost or material estimate. For construction or purchasing, add an appropriate waste allowance separately; the geometric area alone does not account for cuts, overlaps, defects, or installation practice.
Very narrow triangles can be numerically sensitive because a small change in one side or angle can produce a large relative change in area. Recheck any SSS entry close to the triangle-inequality boundary and any SAS or ASA angle close to 0° or 180°. The downloadable workbook preserves canonical numeric values and includes the active inputs, converted outputs, formula, and calculation details.