One formula that handles both increases and decreases
The Universal Formula
Percent Change = ((New Value − Original Value) / Original Value) × 100
If the result is positive, it's an increase.
If the result is negative, it's a decrease.
One formula handles both directions.
Examples
Increase: Price went from $40 to $52
(52 − 40) ÷ 40 × 100
12 ÷ 40 × 100 = +30% (increase)
Decrease: Price went from $40 to $34
(34 − 40) ÷ 40 × 100
−6 ÷ 40 × 100 = −15% (decrease)
Common Mistake: Which Number Goes on the Bottom?
Always divide by the original value — the starting point, the "before" number, the reference. Not the new value, not the bigger number, not the smaller number. The original.
This matters because a change from 50 to 100 is a 100% increase, but a change from 100 to 50 is only a 50% decrease — even though the difference is the same both ways.
💡 Watch for these words: "from" usually marks the original. "From $50 to $75" → original is $50. "Was 200, now 150" → original is 200.
🎯 Practice Problems
1. A value went from 80 to 100. What is the percent change?
A) +20%
B) +25%
C) −20%
D) +80%
2. A value went from 60 to 45. What is the percent change?
A) +25%
B) −25%
C) −15%
D) +15%
3. Temperature changed from 50°F to 50°F. What is the percent change?
A) 100%
B) 50%
C) 0%
D) Cannot determine
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🎯 Bonus Practice
1. A value went from 25 to 75. What is the percent change?
A) +50%
B) +200%
C) +300%
D) +150%
2. A grade dropped from 90 to 72. What is the percent change?
A) −18%
B) −20%
C) +20%
D) −25%
3. Revenue went from $500 to $750. What is the percent change?
A) +50%
B) +250%
C) +33%
D) +150%
4. In the percent change formula, you always divide by the…
A) New value
B) Larger value
C) Smaller value
D) Original value
5. A value went from 200 to 50. What is the percent change?