What is the is-of percentage proportion?
The is-of proportion is a simple cross-multiplication method for solving percentage problems. It is built on the identity \(\frac{\text{Is}}{\text{Of}} = \frac{\text{Percent}}{100}\), where "is" is the part you are talking about, "of" is the whole or total, and "%" is the percentage. Because the equation has three quantities tied together, knowing any two lets you solve for the third.
How to use this calculator
Fill in exactly two of the three boxes — Is (part), Of (whole), and Percent — and leave the value you want to find blank. The calculator detects which field is empty and solves for it automatically using the appropriate rearrangement of the proportion.
The formula explained
Starting from \(\frac{\text{Is}}{\text{Of}} = \frac{\text{Percent}}{100}\), cross-multiply to get \(\text{Is} \times 100 = \text{Of} \times \text{Percent}\). From here:
• To find the part: $$\text{Is} = \frac{\text{Of} \times \text{Percent}}{100}$$
• To find the whole: $$\text{Of} = \frac{\text{Is} \times 100}{\text{Percent}}$$
• To find the percent: $$\text{Percent} = \frac{\text{Is} \times 100}{\text{Of}}$$
Worked example
What is 15% of 200? Here of = 200 and % = 15, and we want "is". Plug in: $$\text{Is} = \frac{200 \times 15}{100} = \frac{3000}{100} = \mathbf{30}$$ So 30 is 15% of 200.
Reverse it: 30 is what percent of 200? $$\text{Percent} = \frac{30 \times 100}{200} = \frac{3000}{200} = \mathbf{15\%}$$
FAQ
Which two fields should I fill? Any two — the empty one is solved. If you fill all three, the percent is recomputed from is and of.
Can the percent be over 100? Yes. If "is" is larger than "of", the percent exceeds 100, which is perfectly valid (e.g., 250 is 125% of 200).
What if I divide by zero? If "of" or "%" is zero where it would be a divisor, the result is reported as 0 to avoid an error.
