How do I find what percent one number is of another?

Divide the part by the whole and multiply by 100: percent = 100 × part / whole. The whole must be non-zero.

How do I calculate what is P% of N?

Multiply N by P/100. For example, 30% of 250 is 250 × 0.30 = 75.

What is the formula for percentage increase and decrease?

Increase: new = base × (1 + p/100). Decrease: new = base × (1 − p/100). The change amount is |new − base| and the change percent is (new − base)/base × 100.

How do I reverse a percentage change to find the original value?

If the final amount is after an increase p%, original = final / (1 + p/100). If the final amount is after a decrease p%, original = final / (1 − p/100).

What if the base or whole is zero?

You cannot divide by zero. For operations that require a 'whole' or 'initial' value, it must be non-zero; otherwise the percentage is undefined.

Can I use decimals or negative numbers?

Decimals are fully supported. Negative values are mathematically valid but consider whether they make sense for your context (e.g., negative revenue is uncommon).

Percentage Calculator

Results

Authoritative Data Source and Methodology

Authoritative source: National Institute of Standards and Technology (NIST), “Guide for the Use of the International System of Units (SI),” NIST Special Publication 811, 2008 (Revised 2008, updates through 2019). See Section 7.10 on the percent (%) as a dimensionless quantity.
Reference: https://physics.nist.gov/cuu/pdf/sp811.pdf

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

1) Percentage of a number: $$x = y \times \frac{p}{100}$$
2) What percent one number is of another: $$p = 100 \times \frac{x}{y} \quad (y \neq 0)$$
3) Increase by percent: $$\text{new} = \text{base} \times \left(1 + \frac{p}{100}\right)$$
4) Decrease by percent: $$\text{new} = \text{base} \times \left(1 - \frac{p}{100}\right)$$
5) Percentage change from A to B: $$\%\Delta = 100 \times \frac{B - A}{A} \quad (A \neq 0)$$
6) Reverse percentage (find original from final): $$\text{original} = \begin{cases} \dfrac{\text{final}}{1 + \frac{p}{100}}, & \text{after increase}\\[6pt] \dfrac{\text{final}}{1 - \frac{p}{100}}, & \text{after decrease} \end{cases}$$

Glossary of Variables

P (%): Percentage rate in percent units. For example, 15% = 15.
N (Base / Whole): The starting amount (or reference whole) before applying a percentage.
x (Result / Part): The outcome of applying a percentage to a base, or the part relative to a whole.
A → B: Initial amount A and final amount B when computing percentage change.
Increase / Decrease amount: The absolute difference between the new and base values.
Original: The value before a known percentage increase or decrease (reverse percentage).

How It Works: A Step-by-Step Example

Increase 240 by 15%

Inputs: Base N = 240; Percentage P = 15.
Apply the formula: new = base × (1 + P/100) = 240 × (1 + 0.15) = 240 × 1.15.
Compute: new = 276.
The increase amount is 276 − 240 = 36, which is 15% of 240.

Frequently Asked Questions (FAQ)

What is the difference between “percent of” and “what percent”?

“Percent of” multiplies a base by a rate (e.g., 25% of 80). “What percent” divides a part by a whole to find a rate (e.g., 20 is what percent of 80?).

Can I compute negative percentages?

Yes, the math is valid. A negative percentage often represents a decrease (e.g., −12%). Ensure this interpretation fits your context.

Why can’t the whole or initial value be zero in some formulas?

Because it would require division by zero, which is undefined (e.g., what percent x is of 0, or percentage change from 0 to B).

How precise are the results?

Results are computed using double-precision arithmetic and formatted for readability. For audits, you can copy exact values and specify your own rounding.

What’s the fastest way to reverse a percentage?

Use the reverse mode. If the final is after a 12% increase, divide by 1.12. If it’s after a 12% decrease, divide by 0.88.

Do I need to press “Calculate”?

No—results update as you type. The button is provided for keyboard and assistive technology workflows.

Is this calculator accessible?

Yes. It follows WCAG 2.1 AA, with keyboard access, visible focus, descriptive labels, and live regions for results and errors.

Tool developed by Ugo Candido. Content verified by the CalcDomain Expert Team.
Strumento sviluppato da Ugo Candido. Contenuti verificati da CalcDomain Expert Team.
Last reviewed for accuracy on: September 13, 2025.