Classic Heron example
13, 14, 15 cmArea = 84 cm^2, perimeter = 42 cm
Triangle Calculator
Check whether three side lengths form a triangle, find the strict possible range for a third side, or calculate SSS area, perimeter, angles, and type with the steps shown.
Side validity checksThird-side rangeAngle estimatesTab-only history
scalene acute triangle84 cm^2
- Perimeter
- 42 cm
- Semiperimeter
- 21 cm
- Triangle inequality margin
- 12 cm
- Angles
- 53.1301023542 degrees, 59.4897625939 degrees, 67.380135052 degrees
Steps
- Check the two shorter sides: 13 + 14 = 27, which is greater than 15 by 12.
- Find semiperimeter: (13 + 14 + 15) / 2 = 21.
- Use Heron's formula: area = sqrt(s(s-a)(s-b)(s-c)).
- The area is 84 cm^2. Angles are found with the law of cosines.
Recent answers
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Geometry answers and history stay in this browser tab while you work.
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How to use the Triangle Calculator
- Choose Check 3 sides when you know all three lengths, or Third-side range when only two lengths are known.
- Use one unit for every entered side and add an optional label such as cm, m, or in.
- Press Calculate triangle to see the exact inequality check or the strict possible range for the missing third side.
- For a valid three-side triangle, review the area, perimeter, angles, type, and inequality margin before copying.
- If you only know base and height, use the Area Calculator. For a 90-degree side problem, use the Right Triangle Calculator.
What people use it for
Check whether three entered side lengths can close into a real triangle.
Find the strict range of possible third-side lengths when two sides are known.
Find the area of a triangle when you know all three side lengths.
Estimate triangle angles with the law of cosines.
Tell whether the triangle is scalene, isosceles, equilateral, acute, right, or obtuse.
Quick examples
Right triangle check
3, 4, 5 mArea = 6 m^2, scalene right triangle
Isosceles triangle
8, 8, 10 inArea is about 31.22 in^2
Sides that cannot close
13.5, 8, 3.5 cmNo triangle because 3.5 + 8 = 11.5, which is not greater than 13.5
Possible third-side range
Known sides 8 and 5The third side must be greater than 3 and less than 13
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Triangle CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
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Frequently asked questions
Quick answers about formulas, units, valid measurements, examples, copying, and private in-browser history.
What can I use the Triangle Calculator for?
Use it when you know all three side lengths and want area, perimeter, semiperimeter, angles, and triangle type in one check.
What formula does the Triangle Calculator use?
It uses Heron's formula for area: s = (a + b + c) / 2, then area = sqrt(s(s-a)(s-b)(s-c)). Angles are estimated with the law of cosines.
What do the main Triangle Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Triangle Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Triangle Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
Can any three side lengths make a triangle?
No. The two shorter sides must add to more than the longest side. For 13.5, 8, and 3.5, the shorter sides total 11.5, so they cannot reach past the 13.5 side and no triangle forms.
How do I find the possible third side when two sides are known?
Choose Third-side range. If the known sides are a and b, the third side c must satisfy |a - b| < c < a + b. Do not include either boundary value; equality makes a flat, zero-area shape.
Do I need the triangle height?
No. This page is for the three-side case. If you know base and height instead, use the Area Calculator triangle mode.
Does this replace a right triangle calculator?
Use this page for any triangle from three sides. Use the Right Triangle Calculator or Pythagorean Theorem Calculator when the problem is only about a 90-degree triangle.
Why are the angles rounded?
The angles come from the law of cosines and are rounded for reading. Tiny decimal differences are normal, but the three angles should add to about 180 degrees.
Does the side order matter?
The area, perimeter, and triangle type stay the same if you swap the side order. The angle labels follow side a, side b, and side c, so keep the order clear if you are matching a drawing.
Can I use decimal side lengths?
Yes. Use positive decimal side lengths when your measurements are not whole numbers, and keep every side in the same unit.
How should I enter units?
Enter the same length unit for every side. The calculator reports perimeter in that unit and area in square units.
Is my triangle history private?
Yes. Recent triangle answers stay only in the current browser tab while you use the page. They are not sent to a server.