% Percentage Calculator

Percentage Calculator — StashGrid

Four modes · Instant results · Calculation history

What is X% of Y?

Result = (Percent / 100) × Number
% of
30
20% of 150 = 30

Calculation History

Working with percentages

Nearly every percentage question is one of four, and this calculator has a mode for each. What follows is the reasoning behind them, plus the handful of places percentages reliably trip people up — including a few where the intuitive answer is simply wrong.

The four basic forms

What is X% of Y? Multiply and divide by 100: 20% of 150 is 150 × 20 ÷ 100 = 30. Equivalently, convert to a decimal first and multiply: 150 × 0.20 = 30. The decimal route is faster once you are comfortable with it.

X is what percent of Y? Divide the part by the whole, then multiply by 100: 30 out of 150 is (30 ÷ 150) × 100 = 20%. Scores work the same way — 45 out of 60 is (45 ÷ 60) × 100 = 75%.

Percentage change. Subtract, divide by the original, multiply by 100: going from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25% increase. Dividing by the new value instead is the most common error here, and it gives 20% — a plausible-looking wrong answer.

Percent to decimal. Divide by 100: 75% = 0.75. Multiply by 100 to go back.

Percent and percentage points are not the same thing

If an interest rate moves from 4% to 5%, it has risen by one percentage point — but that is a 25% increase in the rate itself. Both statements are true and they describe the same event with very different emphasis.

This distinction gets exploited routinely. "Rates up 25%" and "rates up one point" will be chosen depending on which sounds more dramatic. When you see a percentage describing a change in something that is itself a percentage, check which one is meant before drawing a conclusion.

Increases and decreases do not cancel out

Add 50% to 100 and you get 150. Take 50% off 150 and you get 75, not 100. The percentages were applied to different bases, so they do not undo each other.

This matters in a practical way for anything that goes down and then recovers. A 20% loss requires a 25% gain to get back to where you started: 100 falls to 80, and 80 × 1.25 = 100. A 50% loss needs a 100% gain. The deeper the fall, the more lopsided the recovery — which is why drawdowns are described the way they are in finance.

Reverse percentages: finding the original price

An item costs $80 after 20% off. What was the original price? The instinct is to add 20% back, giving $96. That is wrong, because the 20% was taken off the original, not off $80.

The correct method is division. $80 represents 80% of the original, so the original is 80 ÷ 0.80 = $100. Check it: 20% off $100 is $80. ✓

The same logic strips sales tax or VAT from a gross figure. A $107 total including 7% tax has a pre-tax value of 107 ÷ 1.07 = $100, and the tax is $7. Subtracting 7% of $107 gives $99.51, which is wrong by nearly fifty cents on a hundred dollars.

Stacked discounts are smaller than they look

"20% off, then an extra 10% at checkout" is not 30% off. The second discount applies to the already-reduced price: 0.80 × 0.90 = 0.72, so the real saving is 28%. On a $200 item that is $144, not the $140 the headline suggests.

The gap widens as discounts stack. Three successive 20% reductions come to 48.8% off, not 60%. Multiply the remaining fractions rather than adding the discounts, and the answer comes out right every time.

Markup and margin are different numbers

Buy something for $60 and sell it for $100. Both of these are correct:

Same transaction, same $40 profit, two very different-looking percentages. Confusing them is a classic pricing mistake: applying a "40% markup" to a $60 cost gives $84, not the $100 needed to hit a 40% margin. If you need a target margin, divide the cost by (1 − margin): 60 ÷ 0.60 = $100.

Averaging percentages usually gives the wrong answer

Class A has 30 students with an 80% pass rate; class B has 10 students with 40%. The average of 80 and 40 is 60% — but the actual pass rate across both classes is (30 × 80 + 10 × 40) ÷ 40 = 70%.

Percentages can only be averaged directly when the underlying groups are the same size. Otherwise you need a weighted average, or better, go back to the raw counts and recompute from those.

Repeated growth compounds

Something growing 10% a year for three years does not grow 30%. Each year's growth is applied to the previous year's total: 1.10 × 1.10 × 1.10 = 1.331, or 33.1%. Over longer periods the divergence becomes dramatic — 10% for ten years is 159%, not 100%.

The same compounding works against you with repeated declines, which is why a 5% annual fee on an investment costs far more over twenty years than "5% × 20" suggests.

Quick mental shortcuts

Frequently Asked Questions

How do I calculate a percentage of a number?
Multiply the number by the percentage then divide by 100. Example: 20% of 150 = 150 × 20 / 100 = 30. Or simply multiply by the decimal: 150 × 0.20 = 30.
How do I calculate percentage change?
Percentage change = ((New − Old) / Old) × 100. If the result is positive, it's an increase. If negative, it's a decrease. Example: from 80 to 100 = ((100−80)/80) × 100 = 25% increase.
What is X as a percentage of Y?
Divide X by Y, then multiply by 100. Example: 30 is what percent of 150? → (30/150) × 100 = 20%.
How do I convert a percentage to a decimal?
Divide by 100. Example: 75% = 75/100 = 0.75. To convert a decimal back to a percentage, multiply by 100.
How do I find what percent one number is of another?
Use the formula: (Part / Whole) × 100. For example, if you scored 45 out of 60, your percentage is (45/60) × 100 = 75%.
What is the difference between percent and percentage points?
If a rate moves from 4% to 5%, that is a rise of one percentage point but a 25% increase in the rate itself. Both are correct and they sound very different, so check which is meant whenever a percentage describes a change in something that is already a percentage.
If something drops 20%, what increase gets it back to the start?
25%. A 20% fall takes 100 down to 80, and 80 needs a 25% gain to return to 100, because the two percentages are applied to different bases. A 50% loss needs a 100% gain to recover.
How do I find the original price before a discount?
Divide, do not add back. If $80 is the price after 20% off, then $80 is 80% of the original, so the original is 80 ÷ 0.80 = $100. Adding 20% to $80 gives $96, which is wrong.
How do I remove sales tax or VAT from a total?
Divide by 1 plus the tax rate. A $107 total including 7% tax is 107 ÷ 1.07 = $100 before tax, with $7 of tax. Subtracting 7% of $107 gives $99.51, which is close but wrong.
Is 20% off then 10% off the same as 30% off?
No. The second discount applies to the already-reduced price, so 0.80 × 0.90 = 0.72 — a 28% saving, not 30%. Multiply the remaining fractions rather than adding the discounts together.
What is the difference between markup and margin?
Markup is profit as a percentage of cost; margin is profit as a percentage of selling price. Buying at $60 and selling at $100 is a 66.7% markup and a 40% margin — the same $40 profit. To hit a target margin, divide cost by (1 − margin): 60 ÷ 0.60 = $100.
Can I average two percentages together?
Only if the groups behind them are the same size. A class of 30 at 80% and a class of 10 at 40% average to 70% overall, not 60% — you need a weighted average, or better, recompute from the raw counts.
Does 10% growth a year for three years mean 30% growth?
No, it compounds: 1.10 × 1.10 × 1.10 = 1.331, so 33.1%. Over ten years, 10% a year comes to 159% rather than 100%. Each year's growth is applied to the previous total, not to the original.
Is there a trick for calculating percentages in my head?
Start from 10% by moving the decimal one place left, then build: 5% is half of that, 15% is 10% plus half of 10%, 20% is double. It also helps that X% of Y always equals Y% of X — 4% of 75 is the same as 75% of 4, which is just 3.