Triangle calculator guide

How to use the Triangle Calculator

Use this guide when you know the three sides of a triangle, but not the height. The calculator checks whether the sides can make a real triangle, then shows the area, perimeter, angles, and type.

Open the Triangle Calculator
Smoke mascot explaining a 13-14-15 triangle with three side labels, angle arcs, and an area shape.
The guide art follows the same three-side example: 13, 14, and 15 become semiperimeter 21 and area 84. View in the smoke-kawaii gallery

Quick start

  1. Enter side a, side b, and side c using the same unit.
  2. Add a unit label like cm, m, or in if you want the result labels to match your work.
  3. Press Calculate triangle.
  4. Check the area, perimeter, semiperimeter, angle estimates, side type, and angle type before copying.

Best uses

Start here if one of these sounds like your job. The examples below show which inputs matter most.

  • Find the area of a triangle when you know all three side lengths.
  • Check whether three side lengths can close into a real triangle.
  • Estimate triangle angles with the law of cosines.
  • Tell whether the triangle is scalene, isosceles, equilateral, acute, right, or obtuse.

When to use three-side triangle mode

Use the Triangle Calculator when the problem gives you three sides, such as 13 cm, 14 cm, and 15 cm. You do not need the height for this mode.

The calculator first checks the triangle inequality. If one side is too long, like 1, 2, and 3, the sides cannot close into a triangle and the page stops instead of making up an area.

Example: 13, 14, and 15

Enter 13, 14, and 15 with cm as the unit. 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. The angle estimates are all under 90 degrees, so this is a scalene acute triangle.

  • Perimeter: 13 + 14 + 15 = 42 cm.
  • Semiperimeter: 42 / 2 = 21 cm.
  • Area: 84 cm^2.
  • Type: scalene acute triangle.

Example: 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 it as a scalene right triangle.

Reading the answer

Area is shown in square units because it measures the space inside the triangle. If you enter inches, the area is square inches.

Perimeter and semiperimeter stay in the length unit you entered. The side type tells you whether sides match. The angle type tells you whether the triangle is acute, right, or obtuse.

Mistakes to check before trusting it

Do not mix units in one calculation. Convert everything first if one side is in inches and another side is in centimeters.

Do not use this page when you only know base and height. Use the Area Calculator for that job, because Heron's formula needs all three side lengths.

  • If the result says the triangle inequality fails, re-check the side numbers before changing formulas.
  • If your homework uses exact radicals, copy the decimal as a check, not as the final exact form.
  • If a drawing looks right but the numbers fail, one side may be measured from the wrong endpoint.

Sources used for this guide

The page uses standard triangle perimeter, area, and angle rules. These links are useful if you want to compare the formula notes before using the result in homework or a project.

Worked examples for Triangle Calculator

Classic Heron example 13, 14, 15 cm

Area = 84 cm^2, perimeter = 42 cm

Right triangle check 3, 4, 5 m

Area = 6 m^2, scalene right triangle

Isosceles triangle 8, 8, 10 in

Area is about 31.22 in^2

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 sides must pass the triangle inequality. Each pair of sides must add to more than the third side, or the shape cannot close.

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.

Related tools

Keep exploring

If this guide is close but not exact, these links keep you near the same kind of problem.

Privacy and copying results

Recent answers stay visible only while you work in the current browser tab. They are not sent to a server.

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.