Triangle Calculator: Solve Any Triangle in Seconds
Learn how to use the free Triangle Calculator to find area, perimeter, missing sides, and angles — plus master Heron’s formula and the law of cosines.
Table of Contents
Triangles are the most fundamental shape in geometry — and one of the shapes you'll most often need to measure in real life. From roof rafters and stair stringers to garden beds, land plots, and design mockups, triangles show up everywhere. Yet solving one by hand often means juggling several formulas at once: Heron's formula for area, the law of cosines for missing sides and angles, and the law of sines to finish the job.
The free Triangle Calculator removes that juggling act. Give it what you know — three sides, two sides and the included angle, or a base and a height — and it instantly returns the area, perimeter, every missing side and angle, plus a classification of the triangle type. Everything runs 100% client-side in your browser, so results appear instantly and your measurements never leave your device.
In this guide, we'll walk through everything the tool can do, show you how to use it step by step, and explain the mathematics underneath — so you'll not only get answers, but understand why they're right.
Why Use the Triangle Calculator?
- One tool, three input modes. Solve from three sides (SSS), two sides plus the included angle (SAS), or a simple base and height — whichever matches the measurements you actually have.
- A complete solution, not just an area. Alongside area and perimeter, you get all three interior angles and any missing side, so one calculation answers every question about the triangle.
- Instant triangle classification. The calculator automatically identifies whether your triangle is equilateral, isosceles, or scalene — and whether it's right, acute, or obtuse.
- No formulas to memorize. Heron's formula, the law of cosines, and the law of sines are applied for you, correctly, every time.
- 100% private and offline-friendly. All computation happens in your browser. No account, no upload, and no data sent to a server.
- Built-in examples and one-click copy. Load a preset triangle to explore, then copy the full result set straight into homework, quotes, or reports.
Key Features
| Feature | What You Get |
|---|---|
| SSS mode | Enter three sides; get area via Heron's formula, all angles, and perimeter |
| SAS mode | Enter two sides and the included angle; get the third side, area, and remaining angles |
| Base & Height mode | Fast area calculation from base × height ÷ 2 |
| Triangle classification | Equilateral, isosceles, scalene, right, acute, or obtuse — detected automatically |
| Example presets | One-click sample triangles for learning and testing |
| Copy to clipboard | Export every result at once for documents and spreadsheets |
| Reset | Clear inputs and start a new triangle instantly |
- Classification checks sides and angles together. A triangle can be both isosceles and right, for example — the tool reports both properties so nothing is missed.
- Results update as you type. Change any input and the full solution recalculates instantly, which makes it easy to explore "what if" scenarios before committing to a cut or a purchase.
- Invalid inputs are caught early. Side lengths that violate the triangle inequality are flagged instead of producing nonsense numbers.
How to Use
- Open the Triangle Calculator. Visit Triangle Calculator in any browser — no installation or sign-up required.
- Choose your input mode. Pick SSS if you know all three sides, SAS if you know two sides and the angle between them, or Base & Height if you only need the area.
- Enter your values. Type the lengths (and the angle, for SAS) using consistent units. Try an example preset first if you want to see the tool in action.
- Read the full solution. Review the area, perimeter, all three angles, any missing side, and the triangle type classification.
- Copy or reset. Use copy-to-clipboard to save the results into your notes, or hit reset to solve the next triangle.
Understanding Triangle Math
Knowing the math behind the tool helps you pick the right mode and sanity-check every result.
The Three Input Modes
- SSS (three sides): Three side lengths determine exactly one triangle — provided they satisfy the triangle inequality. This mode uses Heron's formula for the area and the law of cosines to recover each angle.
- SAS (two sides + included angle): The "included" angle is the one sandwiched between the two known sides. The law of cosines finds the third side, and the remaining angles follow.
- Base & Height: The fastest route to area alone: A = ½ × base × height. The height must be measured perpendicular to the base.
Heron's Formula
When you know all three sides but no height, Heron's formula computes the area directly. First find the semi-perimeter s = (a + b + c) / 2, then:
Area = √(s(s − a)(s − b)(s − c))
For example, a triangle with sides 3, 4, and 5 has s = 6, giving an area of √(6 × 3 × 2 × 1) = √36 = 6 square units. Heron's formula is what makes SSS mode possible without ever measuring a height.
Law of Cosines
The law of cosines generalizes the Pythagorean theorem to any triangle:
c² = a² + b² − 2ab·cos(C)
Use it to find the third side in SAS mode, or rearranged as cos(C) = (a² + b² − c²) / 2ab, to find any angle when all three sides are known. When C = 90°, the cosine term vanishes and you're left with the familiar a² + b² = c².
Law of Sines
Once one angle and its opposite side are known, the law of sines — a/sin A = b/sin B = c/sin C — quickly finds the remaining angles. The calculator uses it internally to complete the solution, and it's the fastest hand-check for your own results.
Triangle Inequality
Not every set of three lengths forms a triangle. Each side must be shorter than the sum of the other two: a + b > c, and likewise for every pairing. Lengths 2, 3, and 6, for instance, can never meet because 2 + 3 < 6. The calculator validates this rule and warns you before producing results.
Angle Classification
Interior angles always sum to 180°. Based on those angles, a triangle is right (one angle exactly 90°), acute (all angles under 90°), or obtuse (one angle over 90°). Based on its sides, it is equilateral (three equal sides and three 60° angles), isosceles (two equal sides), or scalene (no equal sides). The calculator reports both classifications together.
Practical Use Cases
Construction and DIY
A carpenter framing a gable roof works in triangles constantly. If two rafters each measure 3.5 m and the span between them is 4.8 m, SSS mode returns the roof pitch angles and the exact area of the gable face — useful for ordering siding or sheathing. Deck builders use the same approach to size diagonal bracing.
Education
Students can work homework by hand and then verify each step: enter the same values and compare area, angles, and classification. Teachers use presets to generate quick examples, and curious learners can adjust one side length to watch the angles shift in real time.
Design and Land Measurement
Surveyors have measured land by triangulation for centuries because any irregular plot can be divided into triangles. Measure the three sides of each triangle across a plot, feed them into SSS mode, and sum the areas to estimate the total — no angle measurements required.
Engineering
Triangles are the only inherently rigid polygon, which is why trusses, bridges, and crane booms are built from them. Engineers use SAS and SSS solutions to compute member geometry and load paths; the law of cosines turns physical measurements into the exact angles those designs depend on.
Best Practices
- Keep units consistent. Mixing centimeters and meters silently corrupts every result — convert first, then calculate.
- Check the triangle inequality before trusting field measurements. If your three measured sides fail the test, at least one measurement is off.
- Prefer SAS when you can measure the angle. Two sides and the included angle pin down a triangle uniquely and avoid ambiguity.
- Round only at the end. Carry full precision through intermediate steps; round the final area or length to match your measurement accuracy.
- Sanity-check right triangles with Pythagoras. If the tool says your triangle is right, confirm that a² + b² = c² holds.
- Explore with presets first. Loading an example triangle shows you exactly what each mode expects and returns.
Start Solving Triangles Today
Whether you're cutting rafters, checking homework, estimating a plot of land, or sizing a truss, the Triangle Calculator turns minutes of formula juggling into seconds of typing. Pick your mode, enter what you know, and get the complete picture — area, perimeter, angles, and classification — instantly, privately, and free. Open it now and solve your first triangle in seconds.
Related Tools You Might Like
- Angle Converter — switch between degrees, radians, and other angle units.
- CSS Triangle Generator — create pure-CSS triangles for web projects.
- Ratio Calculator — scale proportions and solve ratio problems.
Happy calculating!