How to Calculate Percentage Increase & Decrease

By ZeroFee Tools · October 15, 2026 · 8 min read

Percentage change is the math behind salary raises, sale prices, stock moves, and rent hikes, yet it is also one of the most miscalculated figures in everyday life. The formulas are short, but the denominator trips people up constantly. The free Percentage Calculator handles the arithmetic instantly, and this guide walks through both formulas with worked examples so you understand exactly what the tool is doing.

You will learn the percentage increase formula, the percentage decrease formula, and the difference between a percent change and a percentage point, each with concrete numbers you can check by hand.

What is percentage change?

Percentage change measures how much a value moved relative to where it started: subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase; a negative result is a decrease.

Percentage change answers the question "how big is this move compared to the starting point?" A $10 price rise means something very different on a $40 item than on a $400 item, and the percentage captures that difference. That is why salaries, investments, discounts, and inflation are all quoted in percentages rather than raw amounts: the percentage normalizes the change so different starting points become comparable.

The single formula covers both directions. When the new value is bigger than the old one, the result is positive and you call it a percentage increase. When the new value is smaller, the result is negative and you call it a percentage decrease. The math does not change; only the sign does. Keeping one formula in your head instead of two is the first step to doing these calculations confidently.

The most common mistake is dividing by the wrong number. The denominator must always be the original (starting) value, because the question is "change relative to what I started with." People who divide by the new value get answers that look plausible but are wrong, sometimes badly wrong on large moves. Every worked example below shows the denominator explicitly so the habit sticks.

The percentage increase formula

Percentage increase equals (new value minus old value) divided by the old value, times 100. A salary rising from $60,000 to $63,000 is a 5% increase: (63,000 - 60,000) / 60,000 x 100.

Write the formula as: % increase = (New - Old) / Old x 100. Start with a clean example. A product costs $40 and the price rises to $50. The difference is $10. Divide by the old price: 10 / 40 = 0.25. Multiply by 100: 25%. The price increased by 25%.

Now a salary example, since raises are the most common real-world case. A salary of $60,000 rises to $63,000. Difference: $3,000. Divide by the original salary: 3,000 / 60,000 = 0.05. Times 100: 5%. Notice how a $3,000 raise can be a 5% raise on $60,000 but only a 2% raise on $150,000. The percentage tells the real story; the dollar amount alone does not.

Large increases have an intuitive check. If the value doubles, that is a 100% increase: (200 - 100) / 100 x 100 = 100%. Tripling is 200%, quadrupling is 300%. If your result says a value doubled but the percentage is 200%, you divided by the wrong number or forgot to subtract the original. The Percentage Calculator shows each step, which makes these checks automatic.

The percentage decrease formula

Percentage decrease uses the same formula: (new value minus old value) divided by the old value, times 100, and the answer comes out negative. A price falling from $80 to $60 is a 25% decrease: (60 - 80) / 80 x 100 = -25%.

The formula is identical: % decrease = (New - Old) / Old x 100. A jacket marked down from $80 to $60 gives (60 - 80) / 80 = -20 / 80 = -0.25, or a 25% decrease. The negative sign is the decrease; in conversation you just say "25% off." Keep the sign in the math, drop it in the words.

Investment examples make the denominator rule vivid. A stock falls from $120 to $108. The drop is $12, and 12 / 120 = 0.10, a 10% decrease. Now reverse it: the stock recovers from $108 back to $120. The gain is $12 again, but 12 / 108 = 0.111, an 11.1% increase. The same $12 move is a different percentage in each direction because the starting point changed. This asymmetry is why a 50% loss needs a 100% gain to recover, and it is the single most useful thing percentage change teaches.

Discounts deserve one caution: a "25% off" sale followed by "an extra 20% off" is not 45% off. The second discount applies to the already-reduced price. On an $80 item: 25% off gives $60, then 20% off $60 gives $48. The total decrease from $80 to $48 is 40%, not 45%. Stacked percentages multiply; they never simply add.

Percentage points vs percent: the distinction that matters

Percentage points measure the simple difference between two percentages, while percent change measures the relative move. Going from 5% to 7% is a 2 percentage point rise but a 40% relative increase.

This distinction causes more confusion than the formulas themselves. Suppose an interest rate moves from 5% to 7%. The straightforward difference is 2, and the correct phrase is "2 percentage points." But the relative change is (7 - 5) / 5 x 100 = 40%. Saying "the rate rose 40%" and "the rate rose 2 percentage points" both describe the same move; only one of them is what a listener usually expects.

News and marketing lean on the ambiguity. A fee rising "by 50%" sounds alarming; rising "by 2 percentage points" sounds mild, and both can be true at once. When you read a claim, check which one is being quoted. When you write one, say which you mean. The habit takes a second and prevents most percentage miscommunication.

The test question: are the two numbers you are comparing already percentages? If yes, and you subtracted them directly, you have percentage points. If you divided the difference by the starting value, you have a percent change. Label the answer accordingly and the confusion disappears.

Step-by-step: calculate any percentage change

Find the difference, divide by the original value, multiply by 100, and label the sign. Those four steps handle increases, decreases, and percentage-point conversions alike.

1. Write down the old and new values. Label them clearly: Old = 40, New = 50. Mixing up which is which is the most common setup error.
2. Subtract: New minus Old. This is the raw change. 50 - 40 = 10. Keep the sign; a negative number means a decrease.
3. Divide by the OLD value. 10 / 40 = 0.25. The denominator is always the starting point, because the change is relative to where you began.
4. Multiply by 100 and add the % sign. 0.25 x 100 = 25%. Positive means an increase of 25%; negative means a decrease.
5. Sanity-check the answer. Doubling is 100%, halving is a 50% decrease, and no change is 0%. If your answer contradicts these anchors, recheck step 3.
6. Verify with the calculator. Run the same numbers through the free Percentage Calculator to confirm your hand calculation in seconds.

6 mistakes to avoid

Almost every percentage error comes from one of six habits: dividing by the new value, adding stacked percentages, confusing points with percent, or rounding too early.

• Dividing by the new value. The denominator is always the original value. Dividing by the new value answers a different question and gives a wrong answer.
• Adding stacked discounts. "25% off plus 20% off" is 40% off total, not 45%. Each percentage applies to a new, smaller base.
• Confusing percentage points with percent. A move from 5% to 7% is 2 percentage points and a 40% relative increase. Name the one you mean.
• Rounding before the final step. Round only the finished percentage. Rounding the difference or the division mid-calculation compounds the error.
• Forgetting the sign. Keep the negative sign through the calculation; it is the only thing distinguishing a decrease from an increase.
• Trusting a big number without a check. A "300% increase" means the value quadrupled. Translate dramatic claims back into plain multiples before believing them.

Frequently asked questions