Daily Life

Percentage Calculator

Q: How do I mentally calculate a 10% discount?

**Move the decimal one place to the left and subtract.** If something costs $1,000, 10% = $100, final price = $900. Or multiply by 0.9: `1,000 × 0.9 = 900`. For 5%, take half of that: $50 off = $950.

Q: Does a 20% increase followed by a 20% discount leave me at the same price?

**No.** `$100 + 20% = $120`. `$120 − 20% = $96`. You lose **4%** in the process. The second percentage is applied to a different (already-changed) base, so they don't cancel out.

Q: How do I calculate percentage change (like a stock gain or price inflation)?

Use `((new − old) / old) × 100`. If a stock went from $80 to $100, the gain is `((100 − 80) / 80) × 100 = **+25%**`. If it went from $100 to $80, the loss is `((80 − 100) / 100) × 100 = **−20%**`. Note: a 25% gain requires a 20% drop to get back — they're not symmetric.

Q: How do I extract sales tax from a price that already includes it?

Divide the total by `(1 + tax rate)`. Example: the bill is $107 and the tax rate is 7%. Pre-tax price = `$107 / 1.07 = $100`. Tax paid = $7. Do NOT calculate 7% of $107 — that gives a wrong answer ($7.49).

Q: What is a 'percentage point' vs a 'percent change'?

If the Federal Reserve raises the federal funds rate from **5.00% to 5.25%**, it raised it by **25 basis points (0.25 percentage points)**. In percentage terms, that's a relative increase of `(0.25 / 5.00) × 100 = **5%**`. News headlines often drop the word 'points' and create confusion.

Q: How do I calculate a selling price to cover cost with a 30% profit margin?

Don't multiply cost by 1.30 — that gives you a 30% **markup** (margin on cost). For a 30% **margin on revenue**, use `price = cost / (1 − margin) = cost / 0.70`. Example: if your cost is $700, the selling price is `$700 / 0.70 = **$1,000**`, and margin = `300 / 1,000 = 30%`.

Q: How do I calculate a stacked or 'extra' discount (e.g. 20% off + an extra 10% off)?

Multiply the remaining-fraction factors: `(1 − 0.20) × (1 − 0.10) = 0.80 × 0.90 = 0.72`. You pay **72% of the original price** — a total discount of **28%, not 30%**. The second discount applies to the already-reduced price, not the original.

Q: How does the US sales tax interact with a percentage discount?

US sales tax is applied **after** any pre-tax discounts in most states. So for a $1,000 item with 20% off and 8% sales tax: step 1) discounted price = `$1,000 × 0.80 = $800`; step 2) add tax = `$800 × 1.08 = **$864**`. Never apply the tax to the original price before the discount.

Q: How do I quickly estimate a 15% or 20% restaurant tip?

**15% tip**: find 10% (move decimal left), then add half of that. On a $48 bill: 10% = $4.80, half = $2.40, total tip = **$7.20**. **20% tip**: find 10% and double it. $4.80 × 2 = **$9.60**. Most phones have a calculator but knowing these shortcuts helps when the check arrives.

Calculate any percentage: discounts, increases, percentage change, and what percent one number is of another. Formula shown step-by-step. Free, no signup.

Data verified · June 2026
Edited by Martín Rodríguez
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How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step

Choose what you want to calculateSelect a mode from the dropdown: 'What is X% of Y', 'Price after discount', 'Price after increase', 'What % is X of Y', or 'Percentage change between two values'.

Enter the first valueType the base number — for example, the original price, initial salary, or starting value. For mode 1 (simple %), this is Y (the base).

Enter the second valueType the percentage or final value — for example, the discount rate (%), the raise percentage, or the ending value.

The percentage (from Latin per centum, 'per hundred') is the workhorse of everyday US math: calculating sales tax at checkout, the 18–20% restaurant tip customary in the US, salary raises, mortgage interest rates from the Federal Reserve, commission, inflation tracked by the Bureau of Labor Statistics (BLS) CPI, and Black Friday discounts. This calculator handles five scenarios: (1) X% of Y, (2) price after a discount, (3) price after an increase, (4) what % is X of Y, and (5) percentage change between two values. It shows the exact formula used — the same operations behind every US credit-card APR statement and paycheck withholding calculation.

When to use this calculator

You're buying something on sale and want to know the exact final price before heading to the register.
You received a job offer with a salary raise of X% and want to calculate your new annual pay.
You're tracking a stock or housing price and want to know the percentage change over time.
You need to split a restaurant bill and add a 20% tip on the pre-tax subtotal.

X% of common amounts

Percent of a number = amount × (percent ÷ 100).

Percent	of 100	of 500	of 1,000	of 5,000
5%	5	25	50	250
10%	10	50	100	500
15%	15	75	150	750
20%	20	100	200	1,000
25%	25	125	250	1,250
50%	50	250	500	2,500

How it works

How It Works

A percentage expresses a number as a fraction of 100. The five modes below cover every common percentage problem.

1. Simple Percentage: What is X% of Y?

result = (Y × X) / 100

Example: What is 15% of $80? → (80 × 15) / 100 = 12.

Equivalently, multiply by the decimal: 80 × 0.15 = 12.

2. Price After Discount

final_price = price × (1 − discount/100)

Example: $1,000 with 20% off → 1,000 × (1 − 0.20) = 1,000 × 0.80 = $800.

3. Price After Increase

final_price = price × (1 + increase/100)

Example: $50,000 salary with a 7% raise → 50,000 × 1.07 = $53,500.

4. What Percentage is X of Y?

percentage = (X / Y) × 100

Example: You scored 42 out of 60 on a test → (42 / 60) × 100 = 70%.

5. Percentage Change Between Two Values

change = ((final − initial) / initial) × 100

Example: Stock went from $120 to $150 → ((150 − 120) / 120) × 100 = +25%.

Negative result = a decrease. Positive = an increase.

Quick Reference Table

Percentage	Fraction	Decimal	Mental Shortcut
5%	1/20	0.05	Divide by 20
10%	1/10	0.10	Move decimal one place left
20%	1/5	0.20	Divide by 5
25%	1/4	0.25	Divide by 4
33%	1/3	0.33	Divide by 3
50%	1/2	0.50	Divide by 2
75%	3/4	0.75	× 3, ÷ 4
100%	1/1	1.00	The number itself

Mental Math Shortcuts

1. 10% of anything: move the decimal point one place left (10% of $350 = $35).
2. 5%: take 10% and divide by 2.
3. 1%: move the decimal two places left (1% of $4,500 = $45).
4. X% of Y = Y% of X: 15% of $80 equals 80% of $15 = $12.
5. Add a percentage: multiply by 1 + rate (e.g., adding 8.5% sales tax: × 1.085).
6. Subtract a percentage: multiply by 1 − rate (e.g., 15% off: × 0.85).

Common Percentage Mistakes

1. Adding percentages directly: a 20% increase then a 20% discount does NOT restore the original price. $100 → $120 → $96. You lose 4%.
2. Confusing change with absolute difference: if something went from $100 to $150, the percentage change is +50%, not just '+50'.
3. Applying % to the tax-included total: if the bill is $108 with 8% tax included, the pre-tax amount is 108 / 1.08 = $100, not 108 × 0.08 = $8.64.
4. Stacked discounts: 20% off + an extra 10% off is NOT 30% off. It's (1 − 0.20) × (1 − 0.10) = 0.72 → 28% total discount.
5. Mixing up percentage points and percent: if the Fed raises rates from 5% to 5.25%, that's 25 basis points (0.25 percentage points), not a 25% increase.

Example: 25% off a $1,200 laptop on Black Friday

Mode: Price after discount.

Value 1 (original price): $1,200.

Value 2 (discount %): 25.

Formula: final_price = price − (price × discount / 100).

Calculation: 1,200 − (1,200 × 25 / 100) = 1,200 − 300 = 900.

Result: final price $900, you save $300 (US state sales tax applies on top of $900 in most states).

With 25% off, you pay $900 and save $300 off the original $1,200 price.

Frequently asked questions

How do I mentally calculate a 10% discount?

Move the decimal one place to the left and subtract. If something costs $1,000, 10% = $100, final price = $900. Or multiply by 0.9: 1,000 × 0.9 = 900. For 5%, take half of that: $50 off = $950.

Does a 20% increase followed by a 20% discount leave me at the same price?

No. $100 + 20% = $120. $120 − 20% = $96. You lose 4% in the process. The second percentage is applied to a different (already-changed) base, so they don't cancel out.

How do I calculate percentage change (like a stock gain or price inflation)?

Use ((new − old) / old) × 100. If a stock went from $80 to $100, the gain is ((100 − 80) / 80) × 100 = +25%. If it went from $100 to $80, the loss is ((80 − 100) / 100) × 100 = −20%. Note: a 25% gain requires a 20% drop to get back — they're not symmetric.

How do I extract sales tax from a price that already includes it?

Divide the total by (1 + tax rate). Example: the bill is $107 and the tax rate is 7%. Pre-tax price = $107 / 1.07 = $100. Tax paid = $7. Do NOT calculate 7% of $107 — that gives a wrong answer ($7.49).

What is a 'percentage point' vs a 'percent change'?

If the Federal Reserve raises the federal funds rate from 5.00% to 5.25%, it raised it by 25 basis points (0.25 percentage points). In percentage terms, that's a relative increase of (0.25 / 5.00) × 100 = 5%. News headlines often drop the word 'points' and create confusion.

How do I calculate a selling price to cover cost with a 30% profit margin?

Don't multiply cost by 1.30 — that gives you a 30% markup (margin on cost). For a 30% margin on revenue, use price = cost / (1 − margin) = cost / 0.70. Example: if your cost is $700, the selling price is $700 / 0.70 = $1,000, and margin = 300 / 1,000 = 30%.

How do I calculate a stacked or 'extra' discount (e.g. 20% off + an extra 10% off)?

Multiply the remaining-fraction factors: (1 − 0.20) × (1 − 0.10) = 0.80 × 0.90 = 0.72. You pay 72% of the original price — a total discount of 28%, not 30%. The second discount applies to the already-reduced price, not the original.

How does the US sales tax interact with a percentage discount?

US sales tax is applied after any pre-tax discounts in most states. So for a $1,000 item with 20% off and 8% sales tax: step 1) discounted price = $1,000 × 0.80 = $800; step 2) add tax = $800 × 1.08 = $864. Never apply the tax to the original price before the discount.

How do I quickly estimate a 15% or 20% restaurant tip?

15% tip: find 10% (move decimal left), then add half of that. On a $48 bill: 10% = $4.80, half = $2.40, total tip = $7.20. 20% tip: find 10% and double it. $4.80 × 2 = $9.60. Most phones have a calculator but knowing these shortcuts helps when the check arrives.

Sources & references

Methodology & trust

Editorial

Daily Life calculator with its formula verified automatically against Khan Academy — Percentages, per our editorial policy and methodology.

Updates

Updated: June 2026. Parameters are verified periodically against the cited sources.

Privacy

Calculations run 100% in your browser. We do not store or transmit your data.

Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

Rodríguez, M. (2026). Percentage Calculator. Hacé Cuentas. https://hacecuentas.com/en/percentage-calculator

Content licensed under CC-BY 4.0 — reuse it citing the source with a link to Hacé Cuentas.

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