How this calculator works
The tool reduces each entered fraction, finds the least common denominator, rewrites the sides with that denominator and adds their numerators. Integer arithmetic keeps the perimeter and triangle inequality exact. Reverse mode subtracts the two known sides from the perimeter before checking the resulting triangle. Repeating decimal output is rounded to ten decimal places and marked with dots.
Formula
P = a+b+c. If a=A/D, b=B/D and c=C/D after choosing a common denominator D, then P=(A+B+C)/D. Missing c=P-a-b; each side must be shorter than the other two together.
Worked example
Sides 1/2, 2/3 and 3/4 become 6/12, 8/12 and 9/12. Their perimeter is 23/12, or 1 11/12 length units. A perimeter of 6 with sides 1 1/2 and 2 leaves a third side of 2 1/2.
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Frequently asked questions
Which units does the answer use?
The same unit as every entered length. Convert mixed units before entering the fractions.
Why use text inputs?
They retain the original numerator and denominator, including values that a decimal numeric field would round.
Can I enter mixed numbers?
Yes. Write 1 1/2 with a space between the whole number and fraction. Decimals such as 1.25 are also exact rational entries.