Triangle Calculator
Find triangle area using three sides, base & height, two sides & angle (SAS), or two angles & a side (AAS)
Results
Area
Perimeter
Side Lengths & Angles
| Measurement | Value |
|---|---|
| Side a | |
| Side b | |
| Side c | |
| Angle A (°) | |
| Angle B (°) | |
| Angle C (°) |
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Triangle Calculator Formula
Three Sides (Heron's Formula): calculate area from all three side lengths.
s = (a + b + c) / 2
Area = √(s × (s−a) × (s−b) × (s−c))
a, b, c are the three side lengths; s is the semi-perimeter.
Base & Height: calculate area from the base and perpendicular height (assumes isosceles triangle).
Area = (base × height) / 2
base is the bottom side length; height is the perpendicular distance from base to apex.
Two Sides & Angle (SAS): calculate area from two sides and the included angle.
Area = (1/2) × a × b × sin(C)
a and b are the two known side lengths; C is the included angle in degrees.
Two Angles & a Side (AAS): calculate area from two angles and the opposite side.
C = 180 − A − B
Area = (a² × sin(B) × sin(C)) / (2 × sin(A))
A and B are the two known angles in degrees; a is the side opposite angle A; C is the derived third angle.
How to Use This Calculator
- Select the tab that matches the measurements you have: Three Sides (SSS), Base & Height, Two Sides & Angle (SAS), or Two Angles & a Side (AAS).
- Enter your known measurements in the input fields shown for that mode.
- Click Calculate to see the area, perimeter, all three side lengths, and all three interior angles.
- Use the share button to copy a link that restores your inputs and result.
Frequently Asked Questions
Which mode should I use?
Choose the tab that matches what you already know: Three Sides if you have all side lengths, Base & Height if you know the base and perpendicular height, Two Sides & Angle (SAS) if you have two sides and the angle between them, or Two Angles & a Side (AAS) if you have two angles and one side length. If you know a right triangle's two legs, you can also use the Pythagorean Theorem calculator to find the hypotenuse first.
Does Base & Height mode work for any triangle?
The Base & Height mode assumes an isosceles triangle — it places the apex directly above the midpoint of the base. If your triangle is scalene (not isosceles), use Three Sides mode or another mode instead.
What is SAS?
SAS stands for Side-Angle-Side. You provide two side lengths (a and b) and the included angle C between them. The calculator uses the formula Area = (1/2) × a × b × sin(C) to find the area and derives all remaining sides and angles.
What is AAS?
AAS stands for Angle-Angle-Side. You provide two angles (A and B) and the length of side a opposite angle A. The calculator derives the third angle as C = 180 − A − B, computes all remaining sides via the law of sines, and then finds the area.
Why must A + B be less than 180° in AAS mode?
The three interior angles of any triangle must sum to exactly 180°. If A + B is 180° or more, no valid third angle C exists and no triangle can be formed.
How do I find the area of a triangle with only the three sides?
Use Three Sides mode, which applies Heron's formula. First compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s × (s−a) × (s−b) × (s−c)). You don't need to know the height — only the three side lengths.
What is Heron's formula?
Heron's formula calculates a triangle's area from its three side lengths alone. With semi-perimeter s = (a + b + c) / 2, the area is √(s × (s−a) × (s−b) × (s−c)). It is named after Heron of Alexandria and is used by this calculator's Three Sides mode.
What is the triangle inequality, and why did I get an error?
The triangle inequality states that the length of any one side must be less than the sum of the other two. If you enter three sides that violate this rule (for example 1, 2, and 10), no triangle can exist, so Three Sides mode shows a form-level error instead of a result.
How do I find the missing angles of a triangle?
Every mode of this calculator reports all three interior angles (A, B, and C in degrees), regardless of which inputs you provide. Three Sides mode derives the angles using the law of cosines; the other modes use the law of sines and the fact that angles sum to 180°.
Does this calculator find the perimeter too?
Yes. Every mode outputs the perimeter (a + b + c) along with the area, all three side lengths, and all three angles — even when you only entered a base and height or two angles and a side.
What units does the triangle calculator use?
The calculator is unit-agnostic and performs no unit conversion. Side lengths come out in whatever unit you enter (inches, cm, meters, etc.), area is in those units squared, and angles are always in degrees.
Can I calculate the area of a right triangle?
Yes. For a right triangle, use Base & Height mode with the two legs as the base and height, or use Three Sides mode if you know all three sides. If you only know two legs and need the hypotenuse first, the Pythagorean Theorem calculator can find it.
What's the difference between SAS and AAS?
SAS (Side-Angle-Side) means you know two sides and the angle between them. AAS (Angle-Angle-Side) means you know two angles and a side. Both fully determine a triangle, but they use different formulas — SAS uses the law of cosines to find the third side, while AAS uses the law of sines.
How can I share my triangle calculation?
After calculating, click the share button to copy a link that encodes your selected mode and input values. Anyone who opens the link sees the same tab active and the same result calculated automatically.