Square Feet of a Triangle Calculator
How it Works
01Pick Mode
Base+Height, SSS, SAS or ASA — based on what you know
02Enter Values
Type dimensions in ft, m, in, yd, cm or angles in deg/rad
03Instant Area
Get square footage using the correct formula for your mode
04Export Report
See m², in², yd², perimeter — download a PDF summary
How to Calculate the Square Footage of a Triangle
Finding the area of a triangle is one of the most common geometry tasks — but it's also one of the most situational. Depending on what you actually measured, there are four different formulas, and using the wrong one gives the wrong answer. This calculator supports all four: Base & Height, Three Sides (SSS via Heron's formula), Two Sides + Included Angle (SAS), and Two Angles + Included Side (ASA).
Just pick the mode that matches the measurements you have, enter the values in whatever units you measured them (feet, metres, inches, yards, centimetres for lengths; degrees or radians for angles), and get the area in square feet instantly — along with conversions to m², in², yd², and the perimeter where applicable.
💡 Four Input Modes, One Answer
Not every triangle situation gives you base and height directly. A surveyor measuring a plot has three side lengths. A carpenter framing a gable has two sides and an angle. An architect from a blueprint has two angles and a side. Each mode uses the correct formula so you never have to convert measurements yourself.
Every input field has an independent unit selector. So if your base is in metres and your height is in feet, enter each as-measured — the calculator converts internally to feet before applying the formula. The result, in square feet, is accurate to four decimal places.
How to Use the Triangle Area Calculator
The Four Triangle Area Formulas
Area = ½ × base × height. The classic formula you learned in school. "Height" means the perpendicular distance from the base to the opposite vertex — not the length of a slanted side. For a triangle with a 10 ft base and a 6 ft height: Area = 0.5 × 10 × 6 = 30 sq ft.
Area = √(s(s − a)(s − b)(s − c)), where s = (a + b + c) / 2 is the semi-perimeter. Used when you've measured all three sides of a plot or object. Works for any triangle, but inputs must satisfy the triangle inequality: each side must be less than the sum of the other two.
Area = ½ × a × b × sin(γ), where γ is the angle between sides a and b. Perfect for surveying or framing where you know two edges and the corner angle between them. For a = 8 ft, b = 10 ft, γ = 60°: Area = 0.5 × 8 × 10 × sin(60°) = 34.64 sq ft.
Area = a² × sin(β) × sin(γ) / (2 × sin(β + γ)), where β and γ are the two angles adjacent to the known side a. Common in blueprints where one side length and two corner angles are given. The sum of β and γ must be less than 180° for a valid triangle.
Example Calculations Across Modes
The same triangle can be calculated from different input sets — here are four equivalent scenarios that all yield the same ~30 sq ft answer:
| Mode | Inputs | Formula | Area (sq ft) |
|---|---|---|---|
| Base × Height | b = 10 ft, h = 6 ft | ½ × b × h | 30.00 sq ft |
| SSS (Heron) | a = 6, b = 10, c = 8 ft | √(s(s−a)(s−b)(s−c)) | 24.00 sq ft |
| SAS | a = 10, b = 6 ft, γ = 90° | ½ × a × b × sin(γ) | 30.00 sq ft |
| ASA | β = 60°, γ = 60°, a = 10 ft | a² · sin(β) · sin(γ) / (2 · sin(β+γ)) | 43.30 sq ft |
Who Uses a Triangle Area Calculator?
Technical Reference
Key Takeaways
Triangle area isn't one formula — it's four, and using the right one depends entirely on what you measured. This calculator eliminates the need to remember which formula applies to which situation. Pick the mode that matches your measurements, and the correct math happens automatically.
Mixed-unit support means your measurements don't need to be uniform. Feet for one side, metres for another, radians for an angle from a blueprint — everything converts internally with exact unit-conversion factors before the formula runs.
For rectangular spaces, use our Square Feet Rectangle Calculator. For circles, trapezoids, and other shapes, visit our Area Calculator. More in the Math & Science Calculators Collection.
Frequently Asked Questions
Which formula should I use for a triangle area?
It depends on what you measured:
- Base & Height — use ½ × b × h (simplest, when you have a perpendicular height)
- Three sides — use Heron's formula: √(s(s−a)(s−b)(s−c))
- Two sides + the angle between them — use SAS: ½ × a × b × sin(γ)
- Two angles + the side between them — use ASA: a² · sin(β) · sin(γ) / (2 · sin(β+γ))
This calculator automatically picks the correct formula once you choose the input mode.
What is Heron's formula?
Heron's formula calculates a triangle's area from only its three side lengths: Area = √(s(s−a)(s−b)(s−c)), where s = (a + b + c) / 2 is the semi-perimeter. Named after Hero of Alexandria (c. 10–70 CE), it's the go-to method when you don't have a perpendicular height or any angles — common in surveying and land measurement.
Does the calculator work for right triangles?
Yes. A right triangle is just a special case: one angle equals 90°. If you know the two legs (the sides forming the right angle), use Base+Height mode — the two legs are exactly base and height. If you know all three sides, SSS mode works. If you have one leg and the hypotenuse with the right angle, SAS with γ = 90° gives you the area directly: ½ × a × b × sin(90°) = ½ × a × b.
Can I mix units between different inputs?
Yes — each length input has its own unit selector (ft, m, in, yd, cm), and each angle input has its own selector (deg, rad). You can enter one side in metres, another in feet, and an angle in radians — the calculator converts all inputs internally to feet and radians before applying the formula. This is especially useful when measurements come from different sources (a field tape measure in feet, a digital plan in metric).
What is the triangle inequality and why does it matter?
The triangle inequality states that any side of a triangle must be less than the sum of the other two sides. If sides are 3, 4, and 9 — there's no triangle, because 3 + 4 < 9. When you use SSS mode, the calculator validates that your three sides can actually form a triangle. If not, you'll see an error explaining the violation — saving you from computing an impossible "area" that would come out as an imaginary number (NaN).
How do I convert angles between degrees and radians?
Degrees → Radians: multiply by π/180 (≈ 0.01745). Radians → Degrees: multiply by 180/π (≈ 57.296). Common equivalents: 30° = π/6 rad ≈ 0.524; 45° = π/4 ≈ 0.785; 60° = π/3 ≈ 1.047; 90° = π/2 ≈ 1.571. You don't need to convert manually — just select the correct unit in the dropdown.
What's the maximum angle I can enter?
A single triangle angle must be less than 180° (or π radians) — at exactly 180°, the triangle collapses into a straight line with zero area. In ASA mode, the sum of the two angles must also be less than 180° — otherwise the third angle would be zero or negative, which is geometrically impossible. The calculator validates this and shows a clear error if your inputs don't form a valid triangle.
Author Spotlight
The ToolsACE Team
Our math tools team calculates triangle area using base-height (A = ½×b×h), three sides via Heron's formula (A = √[s(s-a)(s-b)(s-c)]), SAS (A = ½×a×b×sin(C)), and ASA — with mixed-unit input and output in square feet, square meters, and square inches.