Percent Calculator
Formula: P% × N = (P/100) × N
Formula: (A/B) × 100%
Formula: ((New − Original) / Original) × 100%
Formula: ((B − A) / A) × 100%
Table of Contents
🔹 What Is a Percentage?
A percentage expresses a ratio “per 100.” Writing 37% is the same as 37 out of 100 (i.e., 37/100 or 0.37). Percentages let you quickly compare parts of different-sized wholes—useful in finance, shopping, statistics, and health tracking.
Try our related tools for health and budgeting: BMI Calculator, Calorie Calculator, Body Fat Calculator, BMR Calculator.
🔹 Core Percentage Formulas
- Find P% of N:
(P / 100) × N - What percent is A of B?
(A / B) × 100% - % Increase/Decrease (A → B):
((B − A) / A) × 100% - Find the whole given part & percent:
Whole = Part ÷ (P / 100)
🔹 Worked Examples
| Scenario | Setup | Work | Answer |
|---|---|---|---|
| Find 15% of 200 | P = 15, N = 200 | (15/100) × 200 | 30 |
| What % is 30 of 120? | A = 30, B = 120 | (30/120) × 100% | 25% |
| Price rises from €80 to €92 | Original = 80, New = 92 | ((92−80)/80) × 100% | 15% increase |
| Weight drops from 250 to 212.5 | A = 250, B = 212.5 | ((212.5−250)/250) × 100% | −15% (decrease) |
Want more number tools? Try our Fraction Calculator or Scientific Calculator.
🔹 Common Pitfalls & Tips
- Percent of vs. percent points: From 10% to 12% is a 2 percentage-point rise, which is a 20% increase relative to 10%.
- Two-step discounts compound: 20% off, then 30% off is not 50%—it’s
0.8 × 0.7 = 0.56, i.e., 44% off total. - Divide by the correct base: In “A is what % of B,” B is the base.
- Negative results signal decreases: A negative % change means a drop from the original.
🔹 Converting % ⇄ Decimals ⇄ Fractions
| Form | Convert To | Rule | Example |
|---|---|---|---|
| Percent → Decimal | Decimal | Divide by 100 | 37% → 0.37 |
| Decimal → Percent | Percent | Multiply by 100 | 0.125 → 12.5% |
| Percent → Fraction | Fraction | p% = p/100, then simplify | 25% = 25/100 = 1/4 |
| Fraction → Percent | Percent | (a/b) × 100% | 3/8 = 0.375 = 37.5% |
🔹 Everyday & Business Use Cases
- Shopping: Discounts (e.g., 15% off), VAT additions.
- Finance: Savings rates, loan APR, investment returns (see your Scientific Calculator for quick math).
- Health & Fitness: Body composition changes, calorie adjustments (use the Calorie Calculator).
- Data & Reports: Market share, growth rates, KPIs.
🔹 References & Sources
| Source | Type | What We Used It For | Link |
|---|---|---|---|
| Khan Academy – Percent basics | Educational site | Definitions & foundational examples | khanacademy.org |
| CK-12 – Percent concept | Open textbook | Concept reinforcement & practice styles | ck12.org |
| OECD Data – Percentage change notes | Official data portal | Percentage change usage conventions | data.oecd.org |
| Calculator.net – Percent Calculator | Reference competitor | UI/UX comparison & feature parity | calculator.net |
🔹 FAQ
▾ What’s the quickest way to find P% of a number?
Multiply by
P/100. Example: 18% of 250 = 0.18 × 250 = 45.▾ How do I tell % increase from percentage points?
% increase compares relative change vs. the original. Percentage points measure the absolute difference between two percentages. From 10% to 12% is +2 percentage points, which is a 20% increase relative to 10%.
▾ What percent is A of B if B = 0?
Undefined, because division by zero isn’t allowed. Our calculator will warn you if the base is 0.
▾ Are two consecutive discounts additive?
No. They compound. A 20% discount then 30% discount equals 0.8 × 0.7 = 0.56 → 44% total, not 50%.
▾ How do I reverse a percentage to find the original price?
If €85 is after a 15% discount, original = 85 ÷ 0.85 = €100.
▾ Does the tool accept commas or % signs?
Yes—inputs like “1,200” or “15%” are accepted. We sanitize inputs for you.
▾ Can I calculate negative changes?
Yes. If the new value is lower than the original, the result is a negative percentage, indicating a decrease.