Percent Calculator Formula: How to Work It Out

The percent calculator formula lets you find a percentage of a number, convert a fraction to a percentage, or work out percentage change. You enter two known values, and the calculator returns the third, using the basic relationship: part = (percent / 100) × whole. This page explains the exact formulas, shows a worked example, and covers the common mistakes people make.

Formula

The core percentage formula is:

Part = (Percent / 100) × Whole

Where:

• Part – the amount you are looking for (same unit as the whole).
• Percent – the percentage rate, written as a number (e.g., 20 for 20%).
• Whole – the total or base amount (any unit: dollars, items, people).

Two related formulas come from rearranging this:

• Percent = (Part / Whole) × 100 – use this when you know the part and the whole and want the percentage.
• Whole = Part / (Percent / 100) – use this when you know the part and the percentage and want the total.

For percentage change (increase or decrease from an original value):

Percent change = ((New − Old) / Old) × 100

A positive result means an increase; a negative result means a decrease.

Worked Example

Using the default values from the calculator above: find 20% of 150.

1. Write the formula: Part = (Percent / 100) × Whole
2. Plug in the numbers: Part = (20 / 100) × 150
3. Divide first: 20 / 100 = 0.2
4. Multiply: 0.2 × 150 = 30

The part is 30. The calculator shows this as the headline answer, rounded to two decimals (30.00). The second output, “Percent of whole,” takes the same inputs and computes (20 / 150) × 100 = 13.33%, which is a different question – it asks what percent 20 is of 150. The third output, “Percent change,” treats 150 as the new value and 20 as the old value, giving ((150 − 20) / 20) × 100 = 650% increase. Make sure you pick the output that matches the question you actually have.

When to Use Each Formula

Different situations call for different rearrangements:

• Sales tax or tip: you know the percent and the whole (price), so use Part = (Percent / 100) × Whole to find the tax or tip amount.
• Test scores: you know the part (correct answers) and the whole (total questions), so use Percent = (Part / Whole) × 100 to get the score.
• Reverse percentage: you know the part (e.g., a discounted price) and the percent (e.g., 80% of original), so use Whole = Part / (Percent / 100) to find the original price.
• Growth or decline: you have an old and a new value, so use Percent change = ((New − Old) / Old) × 100.

For example, if a shirt costs $40 and the tax rate is 7%, the tax is (7 / 100) × 40 = $2.80, and the total is $42.80. If you scored 45 out of 60, your percentage is (45 / 60) × 100 = 75%. If a price rose from $50 to $60, the change is ((60 − 50) / 50) × 100 = 20% increase.

Common Mistakes and How to Avoid Them

Percentage problems trip people up in predictable ways:

• Mixing up part and whole. In “what is 20% of 150,” 150 is the whole, not the part. In “what percent is 20 of 150,” 20 is the part. Read the wording carefully.
• Forgetting to divide by 100. The formula uses percent / 100, not the raw percent number. 20% is 0.2, not 20.
• Rounding too early. If you round intermediate steps, the final answer can be off. Keep full precision until the last step, then round to the desired decimal places.
• Confusing percentage points with percent change. A rise from 10% to 15% is a 5 percentage point increase, but a 50% increase relative to the original 10%.
• Using the wrong unit. The part and whole must be in the same unit. If the whole is in dollars, the part is in dollars. If the whole is in kilograms, the part is in kilograms.

Limits of the Formula

The basic percentage formula assumes a simple linear relationship. It does not handle:

• Compound percentages – e.g., a 10% increase followed by a 10% decrease does not return to the original number (100 → 110 → 99). You must apply each step sequentially.
• Percentage points vs. percent – the formula gives a relative percent, not an absolute change in percentage points.
• Negative values – the formula works with negatives, but the interpretation changes. A “−20%” might mean a decrease, but in some contexts it could be a loss or a negative growth rate.
• Zero or negative whole – dividing by zero gives an error; negative wholes can produce confusing results (e.g., a 50% increase on −10 gives −15).

For real-world problems like interest rates or inflation, the simple formula is only a starting point – those usually require compounding or time-based calculations.

How to Use the Calculator Correctly

This calculator has three outputs, but you will usually only need one. Decide which question you are answering first:

1. If you want “what is X% of Y,” enter the percent in the first box and the whole in the second box. Read the first output (Part).
2. If you want “what percent is X of Y,” enter X as the percent box (even though it is not a percent) and Y as the whole box. Read the second output (Percent of whole).
3. If you want “percent change from X to Y,” enter X as the percent box and Y as the whole box. Read the third output (Percent change).

For example, to find 15% of 200, enter 15 and 200, and read 30.00. To find what percent 30 is of 200, enter 30 and 200, and read 15.00%. To find the percent increase from 30 to 200, enter 30 and 200, and read 566.67%.

Frequently Asked Questions

How do I calculate percentage increase?

Subtract the original value from the new value, divide by the original value, and multiply by 100. For example, from 50 to 60: (60 − 50) / 50 × 100 = 20% increase. The result is positive for an increase, negative for a decrease.

What is the formula for reverse percentage?

If you know the part and the percent, the whole is Part / (Percent / 100). For instance, if $30 is 20% of the total, the total is 30 / (20 / 100) = 30 / 0.2 = $150.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator, then multiply by 100. For 3/4, 3 ÷ 4 = 0.75, then 0.75 × 100 = 75%.

What is the difference between percent and percentage points?

A percent is a relative measure (per hundred). A percentage point is the absolute difference between two percentages. If a rate goes from 10% to 15%, it increased by 5 percentage points, but by 50% relative to the original.

Can I use the formula for negative numbers?

Yes, mathematically it works. But interpretation gets tricky – a negative percent change usually means a decrease, and a negative whole can produce counterintuitive results. Always double-check whether a negative answer makes sense in your context.

Why do I get a different answer when I round intermediate steps?

Rounding early introduces error. For example, 20 / 100 = 0.2 is exact, but 1/3 = 0.333… rounded to 0.33 will give a slightly different final result. Keep full precision until the end, then round once.

Related

• Fraction to Percent Calculator: How to Convert
• Convert to a Percent Calculator
• 20% of 25 Questions: Quick Answer & How to Calculate

in p | Percent | % | 20 | 0
in w | Whole | - | 150 | 0
out part | Part | - | (p / 100) * w | 2
out pct | Percent of whole | % | (p / w) * 100 | 2
out change | Percent change | % | ((w - p) / p) * 100 | 2