Triangle Calculator
Calculate triangle area, perimeter and angles.
How to use Triangle Calculator
Enter Triangle Measurements
Input your triangle data in the input fields at the top of the calculator. You can enter either three sides (SSS), two sides and an included angle (SAS), or two angles and a side (AAS). Select the calculation type from the dropdown menu labeled 'Select Calculation Type' before entering values.
Input Values in Correct Units
Type numerical values into each field. Use consistent units throughout (all centimeters, all inches, etc.). The calculator accepts decimal values up to 2 decimal places. Ensure all required fields are filled—empty fields will show a red border indicating missing data.
Click Calculate Button
Press the blue 'Calculate' button located below the input fields. The calculator processes your data instantly without page reload. Results appear in the 'Results' section showing area (square units), perimeter (linear units), and all three angles in degrees.
Review and Copy Results
Check the calculated values displayed in the results panel. Click the 'Copy Results' button to copy all calculations to your clipboard. Use the 'Reset' button to clear fields and start a new calculation.
Related Tools
Triangle calculator: sides, angles, area, and perimeter
Triangle calculator: sides, angles, area, and perimeter
Solve any triangle by entering any three known values at ToolHQ's triangle calculator, get all sides, angles, area, and perimeter instantly. Free, no account required.
A triangle has three sides and three angles that always sum to 180 degrees. If you know any three of those six values (with at least one being a side length), the rest can be calculated. ToolHQ's triangle calculator handles all four standard solving methods: SSS, SAS, ASA, and AAS.
Whether you are a student working through geometry homework, a contractor calculating a roof pitch, or a designer laying out a space, the same formulas apply. Enter what you know and the calculator returns everything else.
Key Takeaways
- Solve any triangle from three known values (sides and/or angles)
- Supports SSS, SAS, ASA, and AAS solving methods
- Outputs include all sides, all angles, area, and perimeter
- Quick formula reference and special triangle ratios included below
- No data is stored or transmitted, all calculations run locally in your browser
How to choose your solving method
The solving method depends on which values you already know. Here is a plain-English guide:
| You know | Method | Approach |
|---|---|---|
| All three sides | SSS (Side-Side-Side) | Law of Cosines to find angles |
| Two sides + included angle | SAS (Side-Angle-Side) | Law of Cosines for third side, then Law of Sines for angles |
| Two angles + included side | ASA (Angle-Side-Angle) | Third angle = 180 - A - B, then Law of Sines for sides |
| Two angles + non-included side | AAS (Angle-Angle-Side) | Third angle = 180 - A - B, then Law of Sines for sides |
The rule for angles: All three interior angles of any triangle always sum to exactly 180 degrees. This means you only ever need two angles to find the third: C = 180 - A - B.
All calculations run locally in your browser, no data is stored or transmitted.
When to use a triangle calculator
Triangle calculations come up in more situations than most people expect:
- Construction and carpentry: Calculating roof pitch, rafter lengths, stair angles, and corner cuts
- Navigation: Finding distances and bearings using triangulation
- Surveying: Measuring land areas and distances using known reference points
- Design and drafting: Laying out angles, clearances, and geometric shapes
- Education: Solving geometry problems involving the Law of Sines, Law of Cosines, and Heron's formula
- Engineering: Calculating forces acting at angles, structural load analysis
Mini-story 1: Ryan was building a garden shed and needed to cut the two rafters for a gabled roof. He knew the width of the shed (4.2 meters), the height of the ridge above the wall plate (1.5 meters), and that the roof was symmetrical. He entered the base half-width (2.1m) and the height (1.5m) as two sides with a 90-degree angle between them (SAS) into ToolHQ's triangle calculator. The result gave him the rafter length (2.57m) and the roof pitch angle (35.5 degrees), both of which he used to make the cuts accurately on the first try.
Calculate triangle dimensions free at ToolHQ
How to use the ToolHQ triangle calculator
- Go to the tool. Navigate to ToolHQ's triangle calculator. No account or sign-up required.
- Select your solving method. Choose SSS, SAS, ASA, or AAS based on what values you have.
- Enter your known values. Input side lengths (in any consistent unit) and angles (in degrees).
- Read the results. The calculator returns all six triangle values (three sides + three angles), plus area and perimeter.
Tip: Keep your units consistent. If sides are in meters, the area will be in square meters and perimeter in meters.
Triangle formula reference table
| Formula | Use case |
|---|---|
| Area = (1/2) x base x height | When you know a base and its perpendicular height |
| Area = (1/2) x a x b x sin(C) | When you know two sides and the included angle |
| Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)) | When you know all three sides (s = semiperimeter) |
| Perimeter = a + b + c | Always |
| Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) | Find a missing side or angle when you have a matching side-angle pair |
| Law of Cosines: c^2 = a^2 + b^2 - 2ab x cos(C) | Find a side from two sides and included angle, or find an angle from three sides |
| Pythagorean theorem: a^2 + b^2 = c^2 | Right triangles only (C = 90 degrees) |
Heron's formula step-by-step: Given sides a = 5, b = 6, c = 7:
- Semiperimeter: s = (5 + 6 + 7) / 2 = 9
- Area = sqrt(9 x (9-5) x (9-6) x (9-7)) = sqrt(9 x 4 x 3 x 2) = sqrt(216) = 14.7 square units
Special triangle ratios
Some triangles have fixed side ratios that come up repeatedly in geometry, construction, and design:
| Triangle type | Angles | Side ratios |
|---|---|---|
| 30-60-90 | 30, 60, 90 degrees | 1: sqrt(3): 2 (approx. 1: 1.732: 2) |
| 45-45-90 (isosceles right) | 45, 45, 90 degrees | 1: 1: sqrt(2) (approx. 1: 1: 1.414) |
| 3-4-5 right triangle | 37, 53, 90 degrees | 3: 4: 5 |
| 5-12-13 right triangle | 22.6, 67.4, 90 degrees | 5: 12: 13 |
The 3-4-5 triangle is frequently used in construction to create perfect 90-degree corners: measure 3 units along one wall, 4 units along the other, and if the diagonal is exactly 5 units, the corner is square.
For related geometry calculations, ToolHQ's circle calculator computes circumference, area, radius, and diameter for any circle, including the circumscribed and inscribed circles of triangles.
Mini-story 2: Dana was working through a trigonometry unit and could not remember when to use the Law of Sines versus the Law of Cosines. Her textbook had two separate sections with no clear "when to use which" rule. She opened ToolHQ's triangle calculator, entered values for an SAS problem (two sides and the included angle), and got the answer along with the formula used. Then she tried an SSS problem and saw the calculator use the Law of Cosines again. The pattern became clear: Law of Cosines for SSS and SAS (when you have a side opposite to the unknown), Law of Sines for ASA and AAS (when you have a matching side-angle pair).
Frequently asked questions
How many values do I need to enter to solve a triangle?
You need exactly three values, and at least one must be a side length. Three angles alone (AAA) do not uniquely define a triangle, they only define its shape, not its size.
What is Heron's formula and when do I use it?
Heron's formula calculates area from all three side lengths, without needing to know any angles or heights. It is useful when you have SSS data and want the area directly: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semiperimeter.
Can a triangle have more than one solution?
The SSA case (two sides and a non-included angle) can produce zero, one, or two valid triangles, depending on the values. This is called the ambiguous case. ToolHQ's calculator identifies which solutions exist and returns all valid triangles.
What is the Law of Cosines?
c^2 = a^2 + b^2 - 2ab x cos(C). It generalizes the Pythagorean theorem to all triangles, when angle C is 90 degrees, cos(C) = 0 and it reduces to the Pythagorean theorem.
Is the triangle calculator free?
Yes. ToolHQ's triangle calculator is completely free, with no account, no sign-up, and no usage limits.
The short version
Any triangle can be solved from three known values (as long as at least one is a side). The four solving methods, SSS, SAS, ASA, AAS, each use the Law of Sines, Law of Cosines, or basic angle arithmetic. For area, you can use base-height, the SAS area formula, or Heron's formula depending on what you know. Special triangle ratios like 30-60-90, 45-45-90, and 3-4-5 appear frequently enough in geometry and construction to be worth memorizing. ToolHQ's calculator handles all four solving methods, outputs all six triangle values plus area and perimeter, and runs entirely in your browser.
For related geometry tools, ToolHQ's circle calculator covers circumference and area calculations, the aspect ratio calculator works with proportional dimensions, and the statistics calculator handles data analysis. Explore more calculator tools at ToolHQ.
Calculate triangle dimensions free at ToolHQ