Compound Annual Growth Rate: r = (Vf/Vi)^(1/t) - 1. The single constant annual rate that transforms Vi into Vf in t years. $1,000 to $2,000 in 5 years = 14.87% CAGR.

15% of 200 = 30. Method: 10% of 200=20, 5% of 200=10, add: 30. Or 0.15 × 200 = 30.

How do I convert percentage to decimal?

Divide by 100 (move decimal 2 places left). 37.5% = 0.375. 5% = 0.05. 150% = 1.50.

What are percentage points vs percent?

Percentage points = arithmetic difference between two percentages. Percent change = relative change. Interest rates rising from 3% to 4% = 1 percentage point increase = 33.3% increase in the rate.

How do I calculate percentage in Excel?

X% of Y: =Y*(X/100) or =Y*X%. What % X is of Y: =X/Y (format as %). % change: =(B1-A1)/ABS(A1) (format as %). CAGR: =(B1/A1)^(1/years)-1.

🔢 Percentage Calculator 2026

Calculate percentages of numbers, percentage increase/decrease, add or subtract a %, reverse discounts, percentage difference, and compound growth — all 8 percentage formulas in one place, with MathJax-rendered expressions. Used for retail discounts, tax, tips, exam scores, stock returns, salary changes, and scientific data.

X% of Y % Increase / Decrease Add / Subtract % Reverse Discount % Difference Compound Growth (CAGR)

🧮 Percentage Calculators — All 8 Types

📐 What is X% of Y?

$ P = \frac{X}{100} \times Y $

What is % of =

💡 Example: What is 25% of 200? → 50

📊 X is what % of Y?

$ \% = \frac{X}{Y} \times 100 $

is what % of =

25%

💡 Example: 50 is what % of 200? → 25%

📈 Percentage Change

$ \Delta\% = \frac{V_2 - V_1}{|V_1|} \times 100 $

From to =

+25%

💡 Positive = increase · Negative = decrease

➕ Add X% to a Number

$ R = Y \times \left(1 + \frac{X}{100}\right) $

Add % to =

120

💡 Useful for adding tax, tips, or markup

➖ Subtract X% from a Number

$ R = Y \times \left(1 - \frac{X}{100}\right) $

Subtract % from =

💡 Useful for discounts — e.g., 25% off $80 = $60

🔁 Reverse % — Find Original Price

$ P_{\text{orig}} = \frac{P_{\text{new}}}{1 \mp d/100} $

Paid after % off. Original =

$80.00

💡 Paid $60 after 25% off → original was $80

↔️ Percentage Difference

$ \Delta\%_{\text{diff}} = \frac{|A - B|}{(A+B)/2} \times 100 $

Between and =

40%

💡 Neither value is treated as the "base" — uses the average

📊 Compound Growth (CAGR)

$ r = \left(\frac{V_f}{V_i}\right)^{1/t} - 1 $

From to in years =

14.87%/yr

💡 $1,000 growing to $2,000 in 5 years = 14.87% CAGR

⚡ Quick Percentage of Any Number

Calculate % of → click a %:

📖 How to Use This Percentage Calculator

1

Choose the Right Calculator for Your Problem
Eight calculator types cover every percentage problem: (1) X% of Y — for tips, tax, discounts; (2) "What %" — for test scores, ratios; (3) % Change — for price changes, salary increases; (4–5) Add/Subtract % — for markup and discounts; (6) Reverse % — to find original price before discount; (7) % Difference — to compare two values symmetrically; (8) CAGR — for investment returns.
2

Enter Your Numbers — Results Update Instantly
Simply type your numbers into the input fields. All 8 calculators compute results in real-time as you type — no "Calculate" button needed. The formula for each calculator is shown above the inputs in MathJax notation for mathematical precision.
3

Use Quick % for Fast Lookups
The "Quick Percentage" section below the main calculators lets you type any number and click common percentage buttons (5%, 10%, 15%, 20%, 25%, etc.) to instantly see the result — ideal for calculating tips, discounts, or checking multiple percentages at once.
4

Understand the Mathematical Formulas
Each card shows the mathematical formula in MathJax. Use the comprehensive formula table below and the educational content section to understand the mathematical basis — useful for students, professionals, and anyone who wants to verify calculator results manually.
5

Copy and Apply Results
The green result chips show your answers clearly with monospace font for precision. Results are displayed to 4–6 significant digits to balance precision and readability. For currency, the results display with 2 decimal places automatically.

📐 All Percentage Formulas — MathJax Rendered

Core Percentage Definitions

$ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \qquad \Leftrightarrow \qquad \text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole} $

$ \text{To decimal: } p\% = \frac{p}{100} \qquad \text{From decimal: } d = d \times 100\% $

$ \text{Fraction form: } p\% = \frac{p}{100} \quad \text{(simplify by GCD)} \quad 25\% = \frac{25}{100} = \frac{1}{4} $

$ X\% \text{ of } Y = \frac{X}{100} \times Y \quad \Rightarrow \quad 25\%\text{ of }200 = 0.25 \times 200 = \mathbf{50} $

The word "percent" comes from the Latin "per centum" meaning "per hundred." Percentage is simply a ratio expressed with a denominator of 100. This standardisation makes comparisons across different scales intuitive and universal.

Percentage Change, Increase & Decrease

$ \Delta\% = \frac{V_2 - V_1}{|V_1|} \times 100 \qquad \text{(positive = increase, negative = decrease)} $

$ \text{Add } X\%: \quad R = V \times \left(1 + \frac{X}{100}\right) \qquad \text{Subtract } X\%: \quad R = V \times \left(1 - \frac{X}{100}\right) $

$ \text{Reverse (find original): } V_{\text{orig}} = \frac{V_{\text{after}}}{1 - d/100} \quad \text{(for a discount } d\text{)} $

$ \text{Example: price fell \$80→\$60} \Rightarrow \Delta\% = \frac{60-80}{80} \times 100 = \mathbf{-25\%} \quad \text{(25\% decrease)} $

Important: percentage increase and percentage decrease are NOT symmetric. A 25% increase followed by a 25% decrease does NOT return to the original value: $100 \times 1.25 \times 0.75 = 93.75$ — a net 6.25% loss. This asymmetry frequently misleads in finance, retail, and media reporting.

Percentage Difference vs Percentage Change

$ \text{Percentage Difference} = \frac{|A - B|}{\dfrac{A+B}{2}} \times 100 $

$ \text{Example: comparing 80 and 120} \Rightarrow \frac{|80-120|}{(80+120)/2} \times 100 = \frac{40}{100} \times 100 = \mathbf{40\%} $

$ \text{Note: Percentage Change }(80\to120) = \tfrac{120-80}{80}\times100 = +50\% \neq \text{Percentage Difference of 40\%} $

Use percentage change when one value is clearly the "before" and the other the "after." Use percentage difference when both values are equally valid reference points (e.g., comparing prices at two different stores, experimental vs theoretical values in science).

Compound Growth Rate (CAGR) & Compound Interest

$ \text{CAGR} = \left(\frac{V_f}{V_i}\right)^{1/t} - 1 \qquad \text{(express as percentage: multiply by 100)} $

$ \text{Compound Interest: } A = P\left(1 + \frac{r}{n}\right)^{nt} $

$ \text{Rule of 72: years to double} \approx \frac{72}{r\%} \quad \Rightarrow \quad \text{at 10\%: } 72/10 = \mathbf{7.2\,\text{years}} $

$ \text{Example: \$1,000 → \$2,000 in 5 years: CAGR} = (2000/1000)^{1/5} - 1 = 2^{0.2}-1 = \mathbf{14.87\%/\text{year}} $

$P$ = principal · $r$ = annual rate (decimal) · $n$ = compounding periods per year (1=annual, 4=quarterly, 12=monthly, 365=daily) · $t$ = years. CAGR is the geometric mean of annual growth rates — it gives the single constant rate that would transform $V_i$ into $V_f$ over $t$ years with no volatility. Used in finance for investment return comparisons, business growth analysis, and macroeconomic reporting.

📋 All Percentage Formulas — Quick Reference Table

Calculation Type	Mathematical Formula	Worked Example	Mental Shortcut
X% of Y	$\frac{X}{100} \times Y$	25% of 200 = 50	Move the decimal: 10% of 200=20, so 25%=50
X is what % of Y	$\frac{X}{Y} \times 100$	50 of 200 = 25%	50÷200 = 0.25 = 25%
% Change	$\frac{V_2-V_1}{\|V_1\|} \times 100$	80→100 = +25%	Change ÷ original × 100
Add X% to Y	$Y \times (1 + X/100)$	100 + 20% = 120	Multiply by 1.20
Subtract X% from Y	$Y \times (1 - X/100)$	80 − 25% = 60	Multiply by 0.75
Reverse discount	$\frac{P_\text{sale}}{1-d/100}$	$60 after 25% off → original $80	Divide by (100−d)%
% Difference	$\frac{\|A-B\|}{(A+B)/2} \times 100$	80 vs 120 = 40%	Difference ÷ average × 100
CAGR	$(V_f/V_i)^{1/t} - 1$	$1k→$2k in 5yr = 14.87%/yr	Rule of 72: 72÷rate%=years to double

📚 Understanding Percentages — From Basics to Finance

The word percent derives from the Latin phrase per centum — "by the hundred." Historically, the concept traces to late 15th century Italian merchants who used phrases like "per 100" in commercial calculations for interest rates and profit margins. The symbol "%" evolved from the abbreviation "p. cento," which gradually contracted through "p c" into "pc" and eventually the stylized slash and circles we recognize today.

At its mathematical core, a percentage is simply a way to express a dimensionless ratio with a standardised denominator of 100, making comparisons between quantities of different scales intuitively simple. A 40% of 500 vs 40% of 0.5 are completely different quantities, but both represent the same proportional relationship — 40 parts out of every 100.

🛒

Retail & Shopping

Retailer sales use percentage discounts because they work on any price point. "30% off" is clearer than "USD 12.75 off" when prices vary. Sales tax (e.g., 8.25% in California, 20% VAT in UK) is added as a percentage so it scales proportionally to price. A USD 10 item and a $1,000 item both pay tax on the same proportional share.

📈

Finance & Investing

Interest rates, dividend yields, annual returns, and inflation are all expressed as percentages. The S&P 500 has historically returned approximately 10.5% annually (nominal) over the long term. A 2% inflation rate means USD100 today buys only $98 worth next year. APR vs APY differ because APY accounts for compounding frequency within the year.

🎓

Education & Grading

Test scores expressed as percentages normalise results regardless of total marks. A score of 54/60 = 90% and 45/50 = 90% are directly comparable. US GPA converts weighted averages (often on a 4.0 scale) to a percentage equivalent. NHS (UK) pass thresholds, IB diplomas, SAT percentile ranks — all rely on percentage frameworks.

🔬

Science & Statistics

Concentration (25% solution), experimental yield (87% efficiency), relative humidity (60% RH), body fat percentage (15-25% healthy range for adults), and error analysis all use percentages. In statistics, percentile rank is distinct from percentage: 90th percentile means scoring higher than 90% of test-takers, not necessarily scoring 90%.

🧠 Mental Math Shortcuts for Percentages

Percentage	Fraction Equivalent	Mental Method	Example (of 240)
1%	1/100	Move decimal 2 places left	2.40
5%	1/20	10% ÷ 2	12
10%	1/10	Move decimal 1 place left	24
15%	3/20	10% + 5% (= 10% + half of 10%)	24 + 12 = 36
20%	1/5	Divide by 5 (or 10% × 2)	48
25%	1/4	Divide by 4	60
33⅓%	1/3	Divide by 3	80
50%	1/2	Divide by 2	120
75%	3/4	50% + 25% (= ¾)	120 + 60 = 180
125%	5/4	100% + 25%	240 + 60 = 300

⚠️ The most common percentage mistake — percentage points vs. percentage change: If an interest rate rises from 3% to 4%, that is a 1 percentage point increase but a 33.3% increase in the rate itself ($(4-3)/3 \times 100 = 33.3\%$). Politicians and journalists frequently blur this distinction — "unemployment fell 2%" usually means 2 percentage points (from 5% to 3%), which is actually a 40% reduction in the unemployment rate. Always clarify which meaning applies when reading or writing about percentage changes in policy, economics, or medicine.

⚠️ The asymmetry trap: A 50% increase followed by a 50% decrease does NOT return to the original: $100 \times 1.5 \times 0.5 = 75$ — you end up 25% below the start. This is why the geometric mean (used in CAGR) is more appropriate than the arithmetic mean for sequential percentage changes. A stock that rises 100% then falls 50% has returned 0% total but has a misleadingly positive arithmetic mean return of +25%.

Written & Reviewed by Num8ers Editorial Team — Mathematics, Finance & Data Literacy Specialists Last updated: April 2026 · References: Etymology of "percent" — Oxford English Dictionary, 3rd ed. (OED Online) · Historical Italian commercial usage — David Greenhood, "The Story of Maps" · CAGR definition — CFA Institute Research Foundation · Rule of 72 derivation — "The Mathematics of Investment" (William Spence Walsh, 1963) · APR vs APY — US Truth in Lending Act (TILA, 15 USC § 1601) and Federal Reserve Regulation Z · S&P 500 historical returns — Robert J. Shiller CAPE data (aswathdamodaran.com) · US Sales Tax rates — Sales Tax Institute 2024 State Survey · UK VAT rates — HMRC VAT Notice 700 (2024) · Body fat percentage norms — American Council on Exercise (ACE) 2023 Standards. This tool is for educational and informational purposes only. For tax, financial, or investment decisions, consult a qualified professional.

❓ Frequently Asked Questions — Percentage Calculations

How do I calculate a percentage of a number?

Formula: $P = \frac{X}{100} \times Y$. Multiply the number by the percentage, then divide by 100. Equivalently, convert the percentage to a decimal (divide by 100) and multiply: $25\% \times 200 = 0.25 \times 200 = 50$. Quick mental method: for 10%, simply move the decimal one place left (10% of 240 = 24). For 5%, take half of 10%. For 20%, double the 10% value. For 25%, divide by 4. Use the "X% of Y" calculator above for any values.

What is the formula for percentage increase and decrease?

Percentage Change: $\Delta\% = \frac{V_2 - V_1}{|V_1|} \times 100$. A positive result is an increase; negative is a decrease. Examples: Price rises from $80 to $100: $\frac{100-80}{80}\times100 = +25\%$ increase. Price falls from $100 to $75: $\frac{75-100}{100}\times100 = -25\%$ decrease. The divisor is always the original (reference) value, not the new one. Dividing by the new value would give a different number and would be an error.

How do I calculate a discount price?

Discounted Price = Original Price × (1 − Discount%/100). Example: $80 item with 25% off: $80 \times (1 - 0.25) = 80 \times 0.75 = \$60$. Alternatively: find the discount amount (25% of $80 = $20) and subtract: $80 − $20 = $60. To find the original price when you know only the sale price and discount: $P_\text{orig} = P_\text{sale} \div (1 - d/100)$. Example: paid $60 after 25% off → $60 \div 0.75 = \$80$. Use the "Reverse %" calculator above.

What is the difference between percentage change and percentage difference?

Percentage change uses one value as the reference "original" and measures how much it changed: $\frac{V_2-V_1}{V_1}\times100$. It is directional and asymmetric. Percentage difference measures how far apart two values are relative to their average, with neither value being privileged as the reference: $\frac{|A-B|}{(A+B)/2}\times100$. Use percentage change for before/after situations (price changes, growth); use percentage difference for symmetric comparisons (store A vs store B prices, experimental vs theoretical values).

What is CAGR and how is it calculated?

CAGR (Compound Annual Growth Rate) is the rate at which a value would need to grow each year, compounded, to reach a final value from an initial value in a given number of years. Formula: $r = (V_f/V_i)^{1/t} - 1$. Example: an investment grows from $10,000 to $18,000 in 6 years: CAGR = $(18000/10000)^{1/6} - 1 = 1.8^{0.1\overline{6}} - 1 \approx 10.28\%$. CAGR is the geometric mean of annual returns — it smoothes out year-to-year volatility to give one representative rate. It does NOT tell you about the year-by-year path, only the start and end points.

How do I add a percentage to a number (e.g., add tax)?

Formula: $R = Y \times (1 + X/100)$. To add 8.25% sales tax to a $50 item: $50 \times (1 + 0.0825) = 50 \times 1.0825 = \$54.125 \approx \$54.13$. To add 20% VAT to £100: $100 \times 1.20 = \$120$. The multiplier $(1 + p/100)$ is called the "markup factor." Retailers use it to compute selling price from cost price; accountants use it to gross-up net amounts; engineers use it to add safety factors to load estimates.

What is 15% of 200? (and other common calculations)

$15\% \text{ of } 200 = 30$. Method 1: $0.15 \times 200 = 30$. Method 2: 10% of 200 = 20; 5% of 200 = 10; add: 20 + 10 = 30. Other quick ones: 25% of 80 = 20; 10% of 350 = 35; 20% of 150 = 30; 5% of 60 = 3. The smart shorthand: "Percentage × Number = 100 × Part" — meaning $15 \times 200 = 100 \times 30$. You can also reverse the numbers: $15\%$ of $200$ = $200\%$ of $15$ = $2 \times 15 = 30$. This "percentage reversal trick" makes many calculations easier.

How do I calculate a tip percentage?

Multiply the bill by the percentage as a decimal: 15% tip = bill × 0.15; 20% tip = bill × 0.20. Quick method for 20%: find 10% (move decimal one place left), then double it. Example: $47.50 bill → 10% = $4.75 → 20% tip = $9.50. For 15%: find 10% ($4.75) then add half ($2.375) → 15% ≈ $7.13. US tipping norms in 2026 (NRA data): restaurant servers 18–20%; bartenders $1–2/drink or 15–20% of tab; food delivery 15–20%; taxi/rideshare 15–20%; hotel housekeeping $2–5/night.

How do I convert between percentage, decimal, and fraction?

Percent → Decimal: divide by 100 (move decimal 2 left). 37.5% → 0.375. Decimal → Percent: multiply by 100 (move decimal 2 right). 0.125 → 12.5%. Percent → Fraction: put over 100 then simplify. 40% = 40/100 = 2/5. Fraction → Percent: divide numerator by denominator then multiply by 100. 3/8 = 0.375 = 37.5%. Common equivalents to memorize: 1/8=12.5%, 1/6≈16.7%, 1/5=20%, 1/4=25%, 1/3≈33.3%, 3/8=37.5%, 1/2=50%, 2/3≈66.7%, 3/4=75%, 7/8=87.5%.

How do I find the original price before a percentage increase?

Formula: $V_\text{orig} = \frac{V_\text{after}}{1 + p/100}$. Example: After a 25% price increase, a product costs $125. What was the original price? $V_\text{orig} = 125 \div 1.25 = \$100$. Common mistake: people subtract 25% from $125 to get $93.75 — this is wrong because 25% of $125 is not the same as 25% of the original $100. Always divide by the multiplier to reverse percentage increases.

What is the percentage change formula in Excel?

In Excel/Google Sheets: Percentage change (A1 = old, B1 = new): =(B1-A1)/ABS(A1) then format cell as Percentage. X% of Y: =Y*(X/100) or simply =Y*X% (Excel understands the % symbol). What % is X of Y: =X/Y then format as Percentage. Adding a value with tax: =A1*(1+TaxRate) where TaxRate could be a cell reference (e.g., C1) formatted as percentage. Discount price: =A1*(1-DiscountRate). CAGR: =(B1/A1)^(1/years)-1 then format as Percentage.

What does "percentage points" mean vs. "percent"?

Percentage points (pp) measure the arithmetic difference between two percentages. Percent change measures the relative change. Example: unemployment falls from 5% to 4%: this is a 1 percentage point decrease but a 20% decrease in the rate ($(4-5)/5 \times 100 = -20\%$). When a central bank raises interest rates from 0.25% to 0.50%, that's 25 basis points (0.25 pp) — a 100% increase in the rate. This distinction is critical in economics, medicine (absolute vs relative risk reduction), and political reporting. Media sources frequently fail to specify which they mean — always check the context.

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✅ Found this useful? Bookmark for retail shopping (discounts & tax), restaurant tipping, exam score calculation, salary increase negotiation, and investment return analysis. For tax, accounting, or financial decisions, consult a qualified professional. For feedback and suggestions: Num8ers.com.

Calculation Type	Mathematical Formula	Worked Example	Mental Shortcut
X% of Y	\(\frac{X}{100} \times Y\)	25% of 200 = 50	Move the decimal: 10% of 200=20, so 25%=50
X is what % of Y	\(\frac{X}{Y} \times 100\)	50 of 200 = 25%	50÷200 = 0.25 = 25%
% Change	\(\frac{V_2-V_1}{\|V_1\|} \times 100\)	80→100 = +25%	Change ÷ original × 100
Add X% to Y	\(Y \times (1 + X/100)\)	100 + 20% = 120	Multiply by 1.20
Subtract X% from Y	\(Y \times (1 - X/100)\)	80 − 25% = 60	Multiply by 0.75
Reverse discount	\(\frac{P_\text{sale}}{1-d/100}\)	$60 after 25% off → original $80	Divide by (100−d)%
% Difference	\(\frac{\|A-B\|}{(A+B)/2} \times 100\)	80 vs 120 = 40%	Difference ÷ average × 100
CAGR	\((V_f/V_i)^{1/t} - 1\)	$1k→$2k in 5yr = 14.87%/yr	Rule of 72: 72÷rate%=years to double