How to Calculate Percentage Change

Q: Can percentage change exceed 100%?

Yes. If a value doubles it is a 100% increase. If it triples it is a 200% increase. A decrease, however, cannot exceed -100% unless the value crosses zero into negative territory.

Q: What is the difference between percentage change and percentage difference?

Percentage change requires a clear starting point -- the original value is the base. Percentage difference compares two equal-status values using their average as the base. Use percentage change for any before-vs-after comparison.

Q: How do I calculate a percentage decrease?

Use the same formula. If the new value is less than the original, the result will be negative, indicating a decrease. Example: from 80 to 60 -- ((60 - 80) / 80) x 100 = -25%, meaning a 25% decrease.

Q: What does a -100% change mean?

A -100% change means the value dropped to zero. Anything lower than -100% means the value has gone negative -- for example, a bank balance that went from $500 to -$100 represents a -120% change.

Q: How do I reverse a percentage change to find the original value?

Divide the new value by (1 + the percentage change expressed as a decimal). If a price increased 25% to reach $75, the original was $75 / 1.25 = $60. For a decrease of 20% that resulted in $80, the original was $80 / 0.80 = $100.

Percentage change measures how much a value has grown or shrunk relative to its starting point. It appears in stock prices, exam scores, sales reports, inflation figures, and almost every before-vs-after comparison.

The percentage change formula

Subtract the original value from the new value, divide by the original value, then multiply by 100. A positive result is an increase; a negative result is a decrease.

% Change = ((New Value - Original Value) / Original Value) x 100

Increase example: A stock goes from $50 to $65. ((65 - 50) / 50) x 100 = 30% increase.

Decrease example: A price drops from $120 to $90. ((90 - 120) / 120) x 100 = -25%. A 25% decrease.

Key insight

The original value is always the denominator. This is what makes percentage change directional -- the same two numbers produce different results depending on which came first.

Step-by-step walkthrough

Breaking the formula into three steps makes it easier to apply without a calculator.

Step 1 -- Find the difference: Subtract the original value from the new value. New - Original. If the result is positive, the value went up. If negative, it went down.

Step 2 -- Divide by the original: Take the difference from Step 1 and divide it by the original value. This gives you the change as a decimal.

Step 3 -- Convert to a percentage: Multiply the decimal by 100. That is your percentage change.

Worked example: A gym membership was $45 per month. It is now $54. Step 1: 54 - 45 = 9. Step 2: 9 / 45 = 0.2. Step 3: 0.2 x 100 = 20% increase.

Common real-world uses

Price changes: A product costs $80 last year and $92 this year. ((92 - 80) / 80) x 100 = 15% price increase. This is exactly what inflation figures measure across a basket of goods.

Revenue growth: Revenue was $40,000 last quarter and $46,000 this quarter. ((46,000 - 40,000) / 40,000) x 100 = 15% growth. Every earnings report in the world uses this formula.

Weight or fitness tracking: Someone weighed 200 lbs and now weighs 185 lbs. ((185 - 200) / 200) x 100 = -7.5%. A 7.5% decrease in body weight.

Test scores: You scored 68 on the first test and 79 on the second. ((79 - 68) / 68) x 100 = 16.2% improvement.

Investment returns: You bought shares at $120 and they are now worth $156. ((156 - 120) / 120) x 100 = 30% gain. This is the total return, not annualized.

Common mistakes to avoid

Dividing by the new value instead of the original: The original value is always the base. Dividing by the wrong number changes both the magnitude and the interpretation of the result.

Confusing percentage change with percentage difference: Percentage difference uses the average of the two values as the base, not the original. Use percentage change when there is a clear before and after. Use percentage difference when the two values have equal status and neither is the starting point.

Reversing the order: The formula is (New - Original) / Original. Reversing it -- (Original - New) / Original -- gives you the right magnitude but the wrong sign, turning an increase into an apparent decrease.

Adding percentage changes together: Two consecutive 50% increases do not equal a 100% increase. After the first 50% increase, the base is larger, so the second 50% is applied to a bigger number. The correct total is 125% -- not 100%.

Why a loss and an equal gain do not cancel out

A drop of 50% followed by a rise of 50% does not put you back where you started. This catches almost everyone the first time, and it is not a quirk of the arithmetic: it follows directly from the fact that the two percentages are calculated on different bases.

Example: $100 falls 50% to $50. It then rises 50%, but 50% of $50 is only $25, so you finish at $75. You are still down 25% from where you began. The loss was measured against $100 and the gain against $50, so the same percentage moved a smaller number of dollars on the way back up.

This is why recovering from a decline always takes a larger percentage than the decline itself:

Gain Needed to Break Even % = (Loss % / (100 - Loss %)) x 100

A 20% loss needs a 25% gain to recover. A 25% loss needs 33.3%. A 50% loss needs 100%. The gap widens sharply as losses get bigger, which is the whole reason large drawdowns are so damaging to an investment even when the percentage sounds survivable.

The same asymmetry applies to prices and salaries. A wage cut of 10% followed by a raise of 10% leaves you 1% below your original pay, not level with it.