Math Tools

Percentage Calculator

Calculate percent of a number, percent change, increases, decreases, discounts, markups, and reverse percentages in one tool.

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Three modes: basic, change, ratio

WHAT IS X% OF Y?

Percentage (%)

Of Number

PERCENTAGE CHANGE

From

X IS WHAT % OF Y?

Percentage Quick Reference

3 questions

How do I calculate a percentage of a number?

Multiply the number by the percentage divided by 100. For example, 15% of 80 = 80 × 0.15 = 12. Use Mode 1 above for this instantly.

How do I calculate percentage change?

Percentage change = ((New − Old) ÷ Old) × 100. If a price rises from $40 to $52, the increase is ((52−40)÷40)×100 = 30%. Use Mode 2 for this calculation.

What is a reverse percentage?

A reverse percentage finds the original value before a percentage was applied. If $13 is 15% of some number X, then X = 13 ÷ 0.15 = $86.67. Mode 3 handles this — useful for finding pre-tax or pre-discount prices.

Math Guide

Percentage Calculator Guide: Percent Change, Discounts, Markups & Reverse Math

A practical guide to all the percentage math you encounter daily — percent of a number, percent change, discounts, markups, tip math, and the reverse-percentage trick that catches most people off guard.

Written by Calculixy Editorial Team · 20 years in financial servicesReviewed for mathematical accuracy and educational clarityUpdated: May 2026

From the Underwriting Desk

Percentages are the most-used and most-misused math in daily life. We see percent signs constantly — on receipts, loan applications, sale tags, weather forecasts, stock tickers, food labels — and we routinely get the arithmetic wrong. The percentage calculator's job is to handle each of the half-dozen distinct percentage operations correctly, including the one most people mess up: reversing a percentage to find the original value. A 20% discount on a $100 item is $80. But if you paid $80 after a 20% discount, the original wasn't $96 — it was $100. That asymmetry trips up everyone until they see why.

What this calculator does

The Percentage Calculator handles every common percentage operation: finding the percent of a number, computing percent change between two values, calculating discounts and final prices, computing markups, and reversing any of these operations to find the missing input. It clearly labels which operation is being performed so you don't have to remember which percentage formula goes where.

Each percentage operation is a single multiplication or division at the core. The complexity comes from knowing which operation matches your question. "20 percent" can mean five different things depending on context: 20% of a number, 20% added to a number, 20% subtracted from a number, the percent change from one number to another, or the reverse of any of those. The calculator removes that decision burden by exposing each operation with its own input fields.

When to use this calculator

Computing a percentage of any number quickly
Calculating percent change (growth, loss, rate of return)
Applying discounts to a price or reversing a sale price to find the original
Adding markup to a cost (retail pricing, contractor estimates)
Computing tip percentages without the touchscreen calculator
Verifying percentages on bills, receipts, or financial statements
Tax calculations when working with mixed pre-tax/post-tax amounts

The five core percentage formulas

1. Percent of a number

Result = Number × (Percent ÷ 100) or equivalently: Result = Number × Percent (as decimal)

20% of $150: 150 × 0.20 = $30. 7.5% of $48: 48 × 0.075 = $3.60.

2. Percent change (between two values)

Percent Change = ((New − Old) ÷ Old) × 100

Going from $100 to $150 is a 50% increase: ((150 − 100) ÷ 100) × 100 = 50%. Going from $150 back to $100 is a 33.3% decrease — not 50% — because the base value changed: ((100 − 150) ÷ 150) × 100 = −33.3%.

3. Discount (percent off)

Final Price = Original × (1 − Discount % ÷ 100) Savings = Original × (Discount % ÷ 100)

$80 with 25% off: 80 × (1 − 0.25) = 80 × 0.75 = $60 final, $20 saved.

4. Markup (percent added)

Final Price = Cost × (1 + Markup % ÷ 100) Markup Amount = Cost × (Markup % ÷ 100)

$40 cost with 60% markup: 40 × 1.60 = $64 sale price, $24 markup.

5. Reverse percentage (find the original)

Original (before discount) = Final ÷ (1 − Discount % ÷ 100) Original (before markup) = Final ÷ (1 + Markup % ÷ 100)

If you paid $60 after a 25% discount, the original was 60 ÷ 0.75 = $80 — not $75. Reversing a percentage requires division, not subtraction.

The asymmetry of percentages: Adding 20% then subtracting 20% does NOT return to the original. $100 + 20% = $120. $120 − 20% = $96. The loss is 20% of $120, not 20% of $100. This asymmetry causes most percentage confusion in everyday life.

Step-by-step example

Buying a discounted item with sales tax

An item is listed at $129.99. It's 30% off. Sales tax is 8%. What's the final cost?

Step 1: Apply the discount

Discounted price = $129.99 × (1 − 0.30) = $129.99 × 0.70 = $90.99

Step 2: Apply sales tax to the discounted price

Tax = $90.99 × 0.08 = $7.28 Final = $90.99 + $7.28 = $98.27

Final cost: $98.27. Compare to the listed $129.99 — total savings of $31.72.

Reversing the example

If you only know the final cost of $98.27 with 8% tax and you want to find the pre-tax discounted price:

Pre-tax = $98.27 ÷ 1.08 = $90.99 ✓

And if you want to confirm the original pre-discount price from the pre-tax amount:

Original = $90.99 ÷ (1 − 0.30) = $90.99 ÷ 0.70 = $129.99 ✓

Percent change vs. percentage points

A common confusion in news reporting and financial discussions:

Percent change

The relative change between two values. Going from 5% to 6% is a 20% increase in percent change terms: ((6 − 5) ÷ 5) × 100 = 20%.

Percentage points

The absolute difference. Going from 5% to 6% is a 1 percentage point increase.

"Interest rates rose from 5% to 6%" is technically a 1 percentage point rise or a 20% relative rise. Headlines and financial commentary often conflate these. When you see "rates rose 20%," check whether it means percentage points or percent change — they're very different numbers.

Compound percentages

Percentages applied repeatedly compound:

Successive percentage changes don't add

An investment that gains 10%, then loses 10%, doesn't return to the original. $100 + 10% = $110. $110 − 10% = $99. You lost $1 even though the percentages were equal in absolute terms.

This is why long-term investing math is dominated by avoiding large losses. A 50% loss requires a 100% gain to recover.

Successive discounts don't sum

"50% off plus an additional 30% off" is not 80% off. It's 50% off, then 30% off the already-discounted price: 0.50 × 0.70 = 0.35, meaning you pay 35% of the original — a 65% discount, not 80%.

The math of compounded percentages matters most in investing, retail discount stacking, and any scenario where percentages are applied in sequence. Multiplying the multipliers (× 0.70 × 0.85 × 0.92...) is faster and more accurate than computing each step separately.

Real-world use cases

1. Shopping discount math

Calculate the final price after a coupon, store discount, or sale. Always confirm whether discounts stack or only one applies — most retailers limit stacking even when their math allows it.

2. Tip calculations

$45 dinner, 20% tip: 45 × 0.20 = $9 tip. Total $54. See our Tip Calculator for tip-specific scenarios including pre-tax vs post-tax bases.

3. Investment returns

If your portfolio went from $50,000 to $55,000, the gain is 10% — calculated as ((55,000 − 50,000) ÷ 50,000) × 100. Use the result with our Compound Interest Calculator to project forward.

4. Salary increase comparison

Two job offers: one promises a 5% raise annually, another offers a 4% raise but with a 5% one-time signing bonus. Convert both to actual dollars at your salary level to compare. A 1% raise difference compounded over years can outweigh a one-time bonus.

5. Statistics and probability

"There's a 75% chance of rain today" is a probability statement, not a measurement of how wet the day will be. Many statistical statements use percentages — interpret them as the share of the relevant population or set, not as a measurement of something else.

6. Markup vs. margin (the business math confusion)

A common business mistake. Markup is calculated against cost; margin is calculated against selling price. The same dollar amount represents a different percentage in each.

Markup = (Selling Price − Cost) ÷ Cost × 100 Margin = (Selling Price − Cost) ÷ Selling Price × 100

$40 cost, $50 selling price: markup = 25% (10 ÷ 40), margin = 20% (10 ÷ 50). Restaurants, retailers, and contractors who confuse these underprice and lose money over time.

Common mistakes

Subtracting a percentage when you should divide. If $80 is the post-discount price after 20% off, the original is $100 (80 ÷ 0.80), not $96 (80 + 16). The reverse of a percentage requires division.
Adding successive percentages. 10% growth one year + 10% growth the next is 21% growth total, not 20%. (1.10 × 1.10 = 1.21).
Confusing percent change with percentage points. A move from 5% to 6% is 1 percentage point but a 20% relative increase. The first sounds small, the second sounds large — both describe the same change.
Mixing up markup and margin. Markup on cost ≠ margin on selling price. A 50% markup is a 33% margin.
Computing tip on post-tax instead of pre-tax. Most etiquette guides suggest pre-tax, but receipts show post-tax. Either is acceptable in practice; just be consistent.
Applying percentages in the wrong order. Discount before tax produces a different result than discount after tax (in most US jurisdictions, discount before tax is standard).
Rounding percentages too aggressively. 19.5% rounded to 20% may seem fine, but in financial calculations involving large amounts, the difference matters.
Mistaking "%" for a fixed amount. A "$20 off" coupon and a "20% off" coupon have very different values depending on the original price. The percentage discount scales; the dollar discount doesn't.

Frequently asked questions

How do I calculate a percentage of a number?

Multiply the number by the percentage as a decimal. 25% of $80 is 80 × 0.25 = $20. To convert a percentage to a decimal, divide by 100: 25 ÷ 100 = 0.25.

What's the formula for percent change?

((New − Old) ÷ Old) × 100. Going from 50 to 75 is a 50% increase. Going from 75 to 50 is a 33.3% decrease (note the asymmetry — the same absolute change is a different percentage depending on the base).

How do I reverse a discount?

Divide the final price by (1 − discount as decimal). $60 after a 25% discount: 60 ÷ (1 − 0.25) = 60 ÷ 0.75 = $80 original. Don't subtract — divide.

What's the difference between markup and margin?

Both describe the relationship between cost and selling price. Markup is calculated relative to cost. Margin is calculated relative to selling price. The same dollar profit represents a higher markup percentage than margin percentage. A 50% markup is a 33.3% margin.

How do I add tax to a price?

Multiply by (1 + tax rate as decimal). $50 with 8% tax: 50 × 1.08 = $54. Our Sales Tax Calculator handles this and the reverse calculation (back out tax from a total) automatically.

Can percentages exceed 100?

Yes. A 200% increase doubles your starting value — so going from $100 to $300 is a 200% increase (because the change of $200 is double the original $100). A 300% gain triples the starting value. A 100% loss eliminates everything; you can't lose more than 100%.

What's the difference between "percent off" and "percent of"?

"30% off $100" means subtract 30% — you pay 70% of $100, which is $70. "30% of $100" means just the 30% — which is $30 (not the price you'd pay). The first is the discount math; the second is the partial value.

How do I split a percentage between people?

If 30% of the work was done collaboratively by 3 people equally, each contributed 10%. If 30% of a tip should be split between a server, busser, and runner, the server gets 20% (or whatever ratio you choose), busser 5%, runner 5%, summing to 30%.

Related Calculixy calculators

From the editorial desk: Percentage math is simple. Percentage intuition isn't. The right way to use a percentage calculator is to verify your mental math, not to replace it. The most common percentage mistakes — confusing percentage points with percent change, reversing a discount by subtraction, forgetting that successive percentages don't add — are all errors of intuition that survive education. Running each calculation through a labeled calculator catches them before they cost money.

Calculixy's Percentage Calculator provides arithmetic results for educational use. Results are mathematically accurate within standard floating-point precision. Always verify percentage calculations in critical contexts (financial decisions, business pricing, legal documents) with multiple sources or a qualified professional. All calculations run locally in your browser; Calculixy does not collect or transmit the values you enter.