Perimeter of a Triangle with Fractions Calculator

How to use this perimeter of a triangle with fractions calculator

What this calculator does

This calculator adds three side lengths and returns the perimeter as an exact reduced fraction, a mixed number when the result is greater than one, and a decimal approximation. It also shows the least common denominator and the equivalent fraction used for each side, so you can audit the arithmetic instead of seeing only a final number. The calculation assumes that all three entries use the same physical unit. It does not convert centimeters to inches or otherwise reconcile mixed units.

When to use it

Use it when a geometry exercise gives fractional side lengths, when a craft or construction sketch uses measurements such as 2 1/5 units, when you want to verify hand addition with unlike denominators, or when you need an Excel record of the exact calculation. The triangle check is useful for spotting side sets that can be added arithmetically but cannot form a non-degenerate triangle.

How to calculate

1. The calculator opens with a complete demonstration: Side a is 2+1/5, Side b is 4/7, and Side c is 15/8. The result and a validated example XLSX workbook are available immediately.
2. Replace each demonstration value with your own side length. Use a whole number, a decimal with a period, a fraction such as 7/8, or a mixed number such as 2+1/5 or 2 1/5.
3. Read the exact Perimeter first. Then use Improper fraction, Decimal approximation, Least common denominator, and the Fraction breakdown table to verify the steps.
4. Select Download Excel to save the current inputs and results. Reset clears the demonstration and all calculated content; Download Excel is then disabled until all three sides contain complete valid values again.

Input guide

Side a, Side b, and Side c are all required positive lengths. Each field accepts digits, one optional decimal point, or a fraction slash. Mixed numbers may use a plus sign or a space between the whole and fractional parts. For example, 2+1/5 and 2 1/5 both mean eleven fifths. A denominator must be a positive integer, a mixed-number numerator must be smaller than its denominator, and values such as 1,5, 1e3, unit symbols, zero, and negative lengths are rejected. Increasing any side increases the perimeter by exactly the same amount. A common mistake is entering measurements in different units; convert them to one unit before calculating.

Output guide

Perimeter is the exact sum of the three sides, displayed as a whole or mixed number. Improper fraction expresses the same exact result as one numerator over one denominator. Decimal approximation is rounded to six decimal places for convenient comparison and should not replace the exact fraction when precision matters. Least common denominator is the least common multiple of the reduced side denominators. The Triangle check reports whether the largest side is smaller than the sum of the other two; equality produces a degenerate straight-line case. In the Fraction breakdown, Entered value preserves what you typed, Reduced fraction is the canonical rational value, Common-denominator form shows the addable equivalent fraction, and Decimal shows the side rounded to six places. OpenStax provides a detailed explanation of adding fractions with different denominators.

Worked example

The demonstration converts 2+1/5 to 11/5 and keeps 4/7 and 15/8 as reduced improper fractions. The least common denominator of 5, 7, and 8 is 280. Rewriting the sides gives 616/280, 160/280, and 525/280. Their numerators total 1,301, so P = 1301/280 = 4 181/280. The decimal display is 4.646429. Because 2.2 is less than 0.571429 + 1.875, the three lengths pass the triangle inequality.