Triangle Perimeter Calculator

What kind of triangle is it?

Choose the kind of triangle you have; the calculator shows the right fields and solves for whatever you leave blank.

Equilateral (one side)

Isosceles (equal sides and base)

Scalene (three sides)

Enter the one side length of an equilateral triangle to get the perimeter, or enter the perimeter to solve for the side.

Side (a)

Perimeter (P)

Please input values into the fields

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The perimeter of a triangle is the sum of all three sides and can be calculated by adding the side lengths together. Select a triangle type and enter values in the triangle calculator to display perimeter and other detailed information about that type of triangle.

There are three input methods corresponding to the relationship between sides. For an equilateral triangle, it is sufficient to measure one side as all sides are equal in length. For an isosceles triangle two equal-length sides and a base are entered. In case of a scalene triangle all three sides have different lengths so all three side lengths must be entered. Regardless of the method chosen, along with perimeter, area, three interior angles and semiperimeter information about whether the triangle is acute, right or obtuse will also be shown.

Three formulas to calculate the perimeter of a triangle:

Equilateral triangle:

Since all sides of an equilateral triangle have the same length, it is enough to measure one side. If we multiply this side length by three, we get the following formula:

P = 3 \, a

If the length of one side is 5 then the perimeter is 15. This method can also be used in reverse. If the perimeter is given, then the tool will calculate the length of a side by dividing by three.

isosceles triangle

An isosceles triangle has two sides of equal length (called the legs) and a third side that can be any length (called the base). To find the perimeter, double the length of the leg and add it to the length of the base.

P = 2 \, a + b

If the length of the legs is 10 and the length of the base is 12 then the perimeter is 32. If you input the perimeter and one side (either the base or a leg) the tool will calculate the missing side.

Scalene triangle

A scalene triangle has three different side lengths, and there's no trick to it - you just add the length of all three sides together.

P = a + b + c

If the length of sides are 4, 5 and 6 then the perimeter is 15. If you leave one side blank and enter the perimeter and two other sides, this tool will calculate the missing side by subtraction.

This is how this calculation tool works:

If you select a triangle type above, the calculator will only show input fields that are relevant for that type of triangle. Enter values and leave the perimeter field blank to calculate the perimeter. Alternatively, enter a perimeter and leave one side blank to calculate the length of the sides backwards. Each input field has its own unit, so you can enter one side in centimeters and another in inches for example. The calculator will convert all values into a common base unit before calculating.

Since the triangle is fully determined by the input side lengths, not only the perimeter but also other information will be shown in the result area. You can open the levels for altitudes and medians or the level for circles to display more detailed information. You can also activate the fence estimate to calculate the costs of fencing off, or use a pie chart of angles and a bar chart of side lengths to get an instant impression of the shape of the triangle.

Derive the whole triangle from the perimeter:

Once all three sides are known the remaining information can be determined. The semiperimeter is half of the perimeter and serves as an input to Heron's formula for calculating the area from the three sides alone, without the need for the height.

s = \frac{P}{2} \qquad A = \sqrt{s\,(s - a)(s - b)(s - c)}

The three interior angles can be calculated using the law of cosines. The angle A opposite side a is given by:

\cos A = \frac{b^2 + c^2 - a^2}{2bc}

The sum of the three interior angles is always 180 degrees. The calculator uses this information to classify a triangle as acute, right or obtuse. It also calculates the in-circle (the radius is obtained by dividing the area by half the perimeter) and the circumcircle which contains the three vertices of the triangle.

Triangle classification by side lengths:

Triangles are named by their side lengths and the classification methods correspond exactly to the three types used in this calculator. If all three sides are equal length it is an equilateral triangle; if exactly two sides are equal length it is an isosceles triangle; if all three sides have different lengths then it is a scalene triangle. An equilateral triangle has the highest symmetry as all sides and angles are equal, with each angle being 60 degrees.

Triangles also have a second name based on their angles. If all the angles are less than 90 degrees then it is an acute triangle; if one of the angles is exactly 90 degrees then it is a right triangle; and if one of the angles is greater than 90 degrees then it is an obtuse triangle. So, for example, a triangle with sides of length 3-4-5 is a right scalene triangle, while a triangle in which all three sides are equal is both equilateral and acute. If the three sides are known this calculator will show both classifications at once.

Perimeter of a right triangle:

Right triangles are a common special case and deserve separate mention. When only the two shorter sides, or legs, of the triangle (a and b) are known, then the third side cannot be determined but can be calculated using the Pythagorean theorem. The hypotenuse is the square root of the sum of the squares of a and b. The perimeter is found by adding all three sides together as follows:

P = a + b + \sqrt{a^2 + b^2}

If the lengths of two sides are 3 and 4, then the length of the hypotenuse is 5 and the perimeter is 12. This is a classic 3-4-5 triangle. If you enter these three sides in the method for scalene triangles, the calculator will check that it is a right triangle and classify it as a right scalene triangle.

Calculation examples:

The table below shows the perimeter of the triangle calculated using three different methods.

Type	You enter	Perimeter
Equilateral	side 5 cm	15 cm
Isosceles	legs 10 cm, base 12 cm	32 cm
Scalene	4, 5, 6 cm	15 cm
Right scalene	3, 4, 5 cm	12 cm

Application examples for the perimeter of a triangle:

When you need to place something around the perimeter of a triangle, then you use the circumference. Tasks like putting up a fence around a triangular flowerbed, edging a flowerbed, installing a triangular window frame or building a gable all require calculating the circumference and multiplying it by the cost per meter. The fence estimation tool provided here performs exactly this calculation. The same perimeter can also be used to determine the length of ribbon required to close a triangular gift box or to calculate the length of trimmings or decorations needed for the edges of triangular flags.

Students learn these three formulas in geometry class and can use this tool to check their homework. Surveyors and construction workers use the formula for scalene triangles when they have a plot of land with three sides that are all different lengths. Because the shape of a triangle is uniquely determined by the lengths of its sides, the perimeter and all other measurements do not change once the side lengths are fixed.

Tips for accurate results:

If possible, use the same unit for each side when measuring them. This is a common source of incorrect answers. Leave all conversions to the calculator. In an isosceles triangle, the two equal sides should be used as legs and the different side should be used as the base. Switching these values will change the shape of the triangle.

If you are using the method for a scalene triangle, make sure that the three lengths can actually create a triangle. The sum of any two sides must be greater than the third side. Even if the calculator adds up your values and calculates perimeter, area and angles will remain blank because no real triangle can be formed.

Frequently asked questions

What is the formula for perimeter of a triangle?

The perimeter is the sum of all three sides, so P = a+b+c. For an equilateral triangle, where all three sides are equal in length, this formula can be simplified to P=3a. For an isosceles triangle, with two sides (a) of equal length and a base (b), the formula becomes P=2a+b. This calculator takes into account these three formulas so you simply enter the values that you have actually measured.

How do you calculate the perimeter of an equilateral triangle?

You multiply one side by three because all sides are the same length. If a side is 5, then the perimeter is 15. You can simply calculate the perimeter by choosing the type of triangle and entering in one side. Alternatively you can enter in the perimeter which will be used to find the length of each side by dividing it by three.

How to calculate the perimeter of an isosceles triangle?

You add the two equal sides and the base together. This means you double one of the equal sides and add the length of the base. P = 2a + b. If the length of the legs is 10 and the base is 12, then the perimeter would be 32. The calculator will solve for the missing side if you enter in the perimeter and any two of the other values.

Can you calculate a missing side if perimeter is known?

Yes. There is a conversion option for each method. For a scalene triangle you can enter the perimeter and two sides leaving the third side blank whereupon the calculator will find it by subtraction. For an equilateral triangle you can calculate the length of one side from the perimeter. For an isosceles triangle you can enter the perimeter and one measurement to get the other measurement.

How do you find the perimeter of a right triangle?

If two sides a and b are known, first calculate the hypotenuse with the Pythagorean theorem. This means that you find the square root of the sum of squares of a and b, then add all three sides together. The perimeter P is given by: P = a + b + (square root of (a² + b²)). If the lengths of both sides are 3 and 4, the hypotenuse will be 5 and the perimeter will be 12. When the three sides are entered in this way, the calculation tool also checks for the right angle of 90 degrees.

Can a triangle always be formed using all three sides?

A triangle can only be formed if the sum of any two sides is greater than the third side. This rule is called the Triangle Inequality Theorem. If the lengths are 1, 1 and 5, then the perimeter is 7 but it is not possible to form a closed triangle. The calculator will report the sum, but indicate that no actual triangle can be formed with these lengths, leaving area and angles blank.

Can this calculator also calculate area?

Yes. As the whole triangle is determined by its three sides, this calculation tool not only calculates the area but also half of the perimeter, the three interior angles, heights and perpendicular bisectors as well as inscribed and circumscribed circles. In addition it estimates the cost for a fence based on the circumference and a price per meter.

Related calculators

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Base of a Triangle CalculatorFind the base of a triangle from its area and height, or from two equal sides, a right-angle hypotenuse, the perimeter, or a side and two angles. Solve for the area or height too.

Triangle Area Calculator (3 Sides)Find the area of a triangle from its three side lengths with Heron's formula, or enter the area with two sides to solve for the third. Also gives the angles, heights, medians, and inscribed and circumscribed circles.

AAA Triangle CalculatorAngle-Angle-Angle triangle calculator: enter two angles to find the third, classify the triangle, and get the exact side ratios. Add one known side and it scales the whole triangle - sides, area, perimeter, heights, and circle radii - in degrees, radians, or gradians.

AAS Triangle CalculatorSolve any AAS (angle-angle-side) triangle: enter two angles and one side and get the third angle, all three sides, the area, perimeter, semi-perimeter, heights, circumradius, and inradius - plus a full triangle classification.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Perimeter
The perimeter of a polygon as the sum of its side lengths, with the triangle case.
Wikipedia: Triangle
Triangle types by side and angle, plus the semi-perimeter, area, and law of cosines.
Math is Fun: Perimeter
Plain-language explanation of perimeter with worked triangle examples.
Wikipedia: Heron's formula
The area of a triangle from its three sides, via the semi-perimeter.