Quick start
- Choose Check 3 sides when you know side a, side b, and side c.
- Choose Third-side range when you know two sides but need the possible values for the third.
- Enter every length in the same unit and add an optional label such as cm, m, or in.
- Press Calculate triangle, then read the strict inequality before copying the area or range.
Best uses
Start here if one of these sounds like your job. The examples below show which inputs matter most.
- 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.
Choose the check that matches your problem
Use Check 3 sides for an SSS problem such as 13 cm, 14 cm, and 15 cm. The calculator tests the triangle inequality first. Valid sides then produce area, perimeter, semiperimeter, three angle estimates, and the triangle type.
Use Third-side range when your problem gives only two lengths. This mode cannot choose one exact third side for you. It shows every length that would let the three sides close into a non-flat triangle.
Can 13.5, 8, and 3.5 form a triangle?
Sort the sides from shortest to longest: 3.5, 8, and 13.5. Add the two shorter sides. Their total is 11.5.
A triangle needs the two shorter sides to add to more than the longest side. Here, 11.5 is less than 13.5, so the ends cannot meet. These lengths do not form a triangle.
- Shorter-side sum: 3.5 + 8 = 11.5.
- Required check: 11.5 > 13.5.
- Result: false, so no triangle forms.
Find the possible third-side range
For known sides a and b, a third side c must be longer than the difference between the known sides and shorter than their sum. Write the rule as |a - b| < c < a + b.
With known sides 8 and 5, the lower boundary is |8 - 5| = 3 and the upper boundary is 8 + 5 = 13. The answer is 3 < c < 13. Do not include 3 or 13 because either boundary makes a flat, zero-area shape.
- Lower boundary: the absolute difference between the known sides.
- Upper boundary: the sum of the known sides.
- Both inequality signs stay strict: greater than the lower value and less than the upper value.
Valid SSS example: 13, 14, and 15
The two shorter sides add to 27, which exceeds the longest side by 12. The sides pass the triangle inequality with room to close.
The perimeter is 42 cm, so the semiperimeter is 21 cm. Heron's formula becomes sqrt(21 x 8 x 7 x 6), which gives an area of 84 cm^2. Every angle is under 90 degrees, so this is a scalene acute triangle.
- Triangle inequality margin: 13 + 14 - 15 = 12 cm.
- Perimeter: 13 + 14 + 15 = 42 cm.
- Semiperimeter: 42 / 2 = 21 cm.
- Area: 84 cm^2.
Right-triangle check: 3, 4, and 5
Enter 3, 4, and 5 with m as the unit. The calculator returns area 6 m^2 and perimeter 12 m.
Because 3^2 + 4^2 = 5^2, the angle across from side 5 is 90 degrees. The page labels the result as a scalene right triangle.
Read the answer without mixing units
Area uses square units because it measures the space inside the triangle. Perimeter, semiperimeter, the inequality margin, and third-side boundaries use the original length unit.
The side type says whether all, two, or none of the side lengths match. The angle type says whether the largest angle is acute, right, or obtuse. Rounded angle estimates should total about 180 degrees.
Mistakes to check before trusting it
Convert mixed units before you enter the sides. A value in inches cannot share one calculation with a value in centimeters.
Use the Area Calculator when you know base and height. Use the Right Triangle Calculator when a 90-degree problem gives only two sides. The SSS mode on this page needs all three side lengths.
- Equality does not pass the side check. Sides 1, 2, and 3 make a flat line, not a triangle.
- The third-side range gives possible values, not one unique missing length.
- If a drawing looks valid but the numbers fail, check whether one side was measured from the wrong endpoint.
Sources used for this guide
These references cover the geometric formulas, triangle inequality range, and Heron area method used in the examples.
Worked examples for Triangle Calculator
Area = 84 cm^2, perimeter = 42 cm
Area = 6 m^2, scalene right triangle
Area is about 31.22 in^2
No triangle because 3.5 + 8 = 11.5, which is not greater than 13.5
The third side must be greater than 3 and less than 13
FAQ in plain language
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.
Related tools
- Area CalculatorCalculate flat-shape area for rectangles, triangles, circles, trapezoids, and parallelograms.
- Right Triangle CalculatorSolve a right triangle from two sides, including the missing side, area, perimeter, and acute angles.
- Pythagorean Theorem CalculatorSolve hypotenuse or missing leg lengths with a^2 + b^2 = c^2 and formula steps.
Keep exploring
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- Free calculator resourcesStart here when you are not sure which calculator page fits.
Privacy and copying results
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Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.