Triangle Calculator - Small Study Tools
SSS · SAS · AAS · ASA · Right Triangle

Triangle Calculator

Solve any triangle. Enter sides, angles or area, get all missing values instantly with an animated diagram. Fully usable on mobile.

All calculations run instantly in your browser, no data sent anywhere
● Pro Version is Free for now
✓ Step-by-step · Unit converter · Type explorer unlocked
Day Night
Heron's Formula
Area = √(s·(s−a)·(s−b)·(s−c)), where s = (a+b+c)/2
🔺 Solve Mode, Choose Your Known Values
Sides
units
units
units
cbaCBA
Please check your inputs, triangle inequality must be satisfied and angles must sum to 180°.
📋 Triangle Basics
1Side a is opposite angle A and side b is opposite angle B, and so on. This naming convention matters for every formula.
2Angles always sum to 180° in any triangle, no exceptions.
3Triangle inequality the sum of any two sides must exceed the third side, or no triangle exists.
🧮 Step-by-Step Working PRO
📏 Area Unit Converter PRO
🔬 Triangle Type Explorer PRO

Click a type to see how it relates to your triangle.

△
Equilateral
All sides equal, all angles 60°
△
Isosceles
Two sides equal, two angles equal
⊿
Right
One angle exactly 90°
▷
Scalene
All sides and angles different
△
Acute
All angles less than 90°
◁
Obtuse
One angle greater than 90°
📖 Quick Reference
1SSS and SAS always determine a unique triangle.
2AAS and ASA also give a unique triangle, since knowing 2 angles fixes the third.
3SSA can be ambiguous two different triangles may fit the same two sides and one non-included angle.
💡 Solving Tips PRO
`; const blob=new Blob([html],{type:'text/html'}); const a=document.createElement('a');a.download='triangle-solution.html';a.href=URL.createObjectURL(blob);a.click(); toast('Downloaded, open it and choose Print then Save as PDF'); }// ── HELPERS ─────────────────────────────────────────────────── function hideError(){const el=document.getElementById('errorBox');el.classList.remove('show');} function toast(msg){const t=document.getElementById('toast');t.textContent=msg;t.classList.add('show');setTimeout(()=>t.classList.remove('show'),2800);}// ── MODE ────────────────────────────────────────────────────── function setMode(mode){ isPro=mode==='pro'; document.getElementById('btnSimple').classList.toggle('active',!isPro); document.getElementById('btnPro').classList.toggle('active',isPro); widget().classList.toggle('pro-mode',isPro); updateTips(); try{localStorage.setItem('sst_tri_mode',mode);}catch(e){} }// ── PRO: TIPS ───────────────────────────────────────────────── function updateTips() { const el = document.getElementById('tipsList'); if (!el) return; const tips = []; if (!lastResult) { tips.push('Solve a triangle above to see tips tailored to your own values.'); } else { tips.push('SSS and SAS always give a unique triangle, but SSA (two sides and a non-included angle) can be ambiguous, sometimes two different triangles fit the same three values.'); tips.push('Side a is always opposite angle A by definition, mixing up which side belongs to which angle is the most common source of wrong answers when solving by hand.'); tips.push('For a right triangle, entering the hypotenuse and one leg is often easier than entering an angle, since angle measurements carry more rounding error than length measurements.'); tips.push('Check your answer with the triangle inequality, the sum of any two sides must be greater than the third, if it is not, the inputs cannot form a real triangle.'); tips.push('The circumradius formula R = abc / 4·Area only needs the three sides, useful as a quick check once you already have the area from Heron\'s Formula.'); } el.innerHTML = tips.slice(0,5).map(t => `
${t}
`).join(''); }// ── INIT ────────────────────────────────────────────────────── updateTips(); try{const m=localStorage.getItem('sst_tri_mode');if(m==='pro')setMode('pro');}catch(e){}

How to Use the Triangle Calculator

From what you already know to a complete solution in seconds. Fully usable on mobile.

1
Choose Solve Mode
Pick SSS, SAS, AAS, ASA, or Right Triangle based on what you know.
2
Enter Known Values
Type in the sides or angles you already have.
3
See the Diagram
Watch your triangle draw itself with every side and angle labeled.
4
Copy or Go Pro
Copy the results or download a PDF, or unlock step by step working in Pro.

Every calculation runs inside your own browser. No account, no tracking, nothing ever uploaded.

Specifications
Price Free
Data Handling Never leaves your browser
Solve Modes SSS · SAS · AAS · ASA · Right Triangle
Pro Features Steps · Unit Converter · Type Explorer
Platform Optimized for Web & Mobile
Built by SmallStudyTools.com
Found a bug or something not working right? Let us know and we'll fix it. Every report helps make this tool better.
Report an Issue

Triangle Calculator, Free and Online

A triangle calculator finds every missing side and angle once you supply enough known values, using the Law of Cosines, the Law of Sines or Heron's Formula depending on what you already know. This one solves from three sides, two sides and an angle, two angles and a side, or a right triangle, with an animated diagram and runs entirely inside your browser.

Not every triangle problem gives you the same starting information, which is why a genuinely useful triangle calculator needs more than one solving method. This tool covers all of them, whether you are looking for a right triangle angle calculator, an area of triangle calculator, or a right triangle side calculator. Choose SSS if you know all three sides, SAS if you know two sides and the included angle, AAS or ASA if you know two angles and a side, or the dedicated right triangle mode for Pythagorean theorem problems, area of a right triangle included. Enter your known values and every side, angle, the area, the perimeter, the inradius and the circumradius appear instantly, along with an animated diagram showing your exact triangle, including the triangle height and every median. Pro Mode adds full step by step working for every calculation, an area unit converter, and a triangle type explorer that compares your triangle against equilateral, isosceles, right, scalene, acute and obtuse classifications.

Heron's Formula
Area = √(s·(s−a)·(s−b)·(s−c)), where s = (a+b+c)/2

Once you know all three side lengths, Heron's Formula finds the area directly, no angles required. This calculator computes it automatically in SSS mode, and derives it internally from the sides in every other mode too.

1Simple vs Pro, What Each Mode Includes

FeatureSimple ModePro Mode (Free)
SSS, SAS, AAS, ASA and right triangle solvingIncludedIncluded
Animated triangle diagram with labeled sides and anglesIncludedIncluded
Area, perimeter, inradius, circumradius, heights and mediansIncludedIncluded
Full step by step working for every calculationNot includedIncluded
Area unit converterNot includedIncluded
Triangle type explorer and comparisonNot includedIncluded
Copy results and download PDFIncludedIncluded

2Which Solve Mode Do You Need

SSS, 3 Sides Known
Heron's Formula plus Law of Cosines
SAS, 2 Sides + Included Angle
Law of Cosines, then Law of Sines
AAS or ASA, 2 Angles + a Side
Third angle from 180°, then Law of Sines
Right Triangle
Pythagorean theorem, any 2 known values

This tool also works well as an isosceles triangle calculator, an equilateral triangle calculator, or a special right triangle calculator, since all of those are simply triangles with extra known constraints. An equilateral triangle always has three equal sides and three 60 degree angles, so entering any one side in SSS mode solves the rest instantly. An isosceles triangle has exactly two equal sides, which SSS or SAS mode handles the same way as any other triangle. A special right triangle calculator typically means a 30 60 90 or 45 45 90 triangle, both of which the right triangle mode here solves from a single known side using the Pythagorean theorem and fixed angle relationships, no special formulas needed beyond what is already built in.

The mistake that trips up the most students is mixing up which side belongs to which angle. Side a is always opposite angle A, side b is always opposite angle B, and side c is always opposite angle C, this naming convention is the backbone of every formula on this page. A second common source of confusion is the SSA case, two sides and a non included angle, which is genuinely ambiguous in some situations and can produce two different valid triangles from the same three numbers, unlike SSS, SAS, AAS and ASA, which always determine a single unique triangle.

3Where Triangle Solving Actually Mattered

The same method this calculator uses, measuring a triangle from a known baseline and its angles, once mapped an entire mountain range without anyone setting foot on the summit. According to Britannica's account of the Great Trigonometric Survey of India, surveyors between 1800 and 1913 measured a single baseline of known length, then used angles taken with a theodolite from each end to solve triangle after triangle across the entire subcontinent, chaining thousands of triangles together into what became known as the Great Arc. That triangulation network eventually reached the Himalayas, and it was the Indian mathematician Radhanath Sikdar, working from the survey's own trigonometric calculations, who first determined that Peak XV, later renamed Mount Everest, was the tallest mountain on Earth. No one climbed it to find that out, they solved triangles.

QuestionQuick Answer
What was the Great Trigonometric Survey?A triangulation survey of the Indian subcontinent, 1800 to 1913
What method did it use?Solving chained triangles from a known baseline and measured angles
Who first identified Everest as the tallest peak?Radhanath Sikdar, using the survey's trigonometric calculations
Did surveyors climb the mountain to measure it?No, the height came entirely from triangulation
Privacy Note

Every calculation runs inside your own browser using JavaScript, nothing is uploaded or sent to a server, and no account or signup is required.

4Frequently Asked Questions

How do I use this triangle calculator?
Pick the solve mode that matches what you already know, three sides (SSS), two sides and the angle between them (SAS), two angles and a side (AAS or ASA), or a right triangle. Enter your known values and press Calculate Triangle to see every side, every angle, the area and the perimeter instantly.
How do I find the area of a triangle calculator style, from three sides?
Use Heron's Formula. Add the three sides and divide by two to get the semi perimeter s, then the area equals the square root of s times s minus a, times s minus b, times s minus c. This calculator applies that formula automatically in SSS mode.
What is a 30 60 90 triangle calculator actually calculating?
A 30 60 90 triangle is a special right triangle where the side lengths always follow a fixed ratio, 1 to the square root of 3 to 2. Enter any one side in the right triangle mode here and the other two sides and both remaining angles follow automatically from that fixed relationship.
How do I find the hypotenuse of a triangle calculator style?
For a right triangle, the hypotenuse is the longest side, opposite the 90 degree angle. Enter the two legs in the right triangle mode and this triangle hypotenuse calculator applies the Pythagorean theorem automatically, hypotenuse squared equals leg a squared plus leg b squared.
What is the triangle side calculator method for a triangle that is not a right triangle?
For any triangle that is not a right triangle, use the Law of Cosines or the Law of Sines depending on what you already know. This calculator picks the right method automatically once you choose the SSS, SAS, AAS or ASA solve mode that matches your known values.
Can this also work as an area of a right triangle calculator or a triangle height calculator?
Yes. Once a right triangle is solved, the area, the height to each side and every median are calculated automatically and shown in the complete solution table, no separate tool or extra steps needed.
Is my triangle data private when I use this calculator?
Yes. Every calculation runs inside your own browser using JavaScript, nothing is uploaded or sent to a server, and no account or signup is required.

Grounded in Britannica's own account of the Great Trigonometric Survey of India, not the assumption that triangulation is purely a classroom exercise. The full account is available on Britannica's website. For related tools on this site, see the Scientific Calculator and the full SmallStudyTools.com tool library.

More Math Tools

Every other tool in the Math Tools category

Scientific Calculator Full-function calculator for trig, exponents, and more
Quadratic Equation Solver Find the roots of any quadratic equation instantly
Logarithm Calculator Evaluate, convert, solve for x and differentiate logs
Binomial Probability Calculator Calculate probabilities for a binomial distribution
Number Base Converter Convert between binary, decimal, hex, and octal
Lilly
Here to help you find a tool
Search tools Search blogs
Try me to find a tool! 👋