To find percent change, use this formula: ((New Value − Old Value) ÷ Old Value) × 100 how to calculate voltage drop. Subtract the old value from the new value, divide the result by the old value, then multiply by 100. A positive answer means a percent increase; a negative answer means a percent decrease. For example, if a price rises from $40 to $50, the percent change is (($50 − $40) ÷ $40) × 100 = 25%.

Percent change shows up everywhere: sale discounts, salary raises, investment returns, population growth, and grade improvements. It answers the question “how much did this change relative to where it started?” — which is far more useful than the raw dollar or point difference. A $10 raise means something very different on a $40 bill versus a $4,000 bill, and percent change captures that difference.

The Percent Change Formula, Explained

The formula has three moving parts, and each one matters:

New Value − Old Value: This gives you the raw change (the difference). If the new value is bigger, this number is positive. If it is smaller, the number is negative — and that negative sign is important, so do not drop it.

÷ Old Value: Dividing by the old value (not the new one) is the step most people get wrong. Percent change is always measured relative to the starting point. A price going from $50 to $40 is a 20% decrease (($40 − $50) ÷ $50 = −0.20), not a 25% decrease.

× 100: This converts the decimal to a percentage. 0.25 becomes 25%.

Memorize it as a sentence: difference divided by original, times one hundred. Google Sheets users can also compute it directly in a spreadsheet — Google’s formula documentation covers the functions you will need.

Step-by-Step Example: Percent Increase

Say your rent goes from $1,200 to $1,350 per month. What is the percent increase?

Step 1: Find the difference: $1,350 − $1,200 = $150.

Step 2: Divide by the old value: $150 ÷ $1,200 = 0.125.

Step 3: Multiply by 100: 0.125 × 100 = 12.5%.

Your rent increased by 12.5%. Notice how the raw $150 figure does not tell the full story — 12.5% instantly communicates the scale of the hike.

Step-by-Step Example: Percent Decrease

Now say a laptop drops from $899 to $674 during a sale. What is the percent decrease?

Step 1: Find the difference: $674 − $899 = −$225.

Step 2: Divide by the old value: −$225 ÷ $899 = −0.2503.

Step 3: Multiply by 100: −0.2503 × 100 = −25.03%, or roughly a 25% decrease.

The negative sign tells you it is a decrease. In everyday language you would just say “25% off,” but keeping the sign straight matters when you chain calculations together.

Common Percent Change Mistakes

Dividing by the new value instead of the old

This is the number-one error. Percent change always uses the original value as the baseline. Going from 80 to 100 is a 25% increase ((100−80)÷80), not 20%.

Confusing percentage points with percent change

If an interest rate rises from 4% to 6%, that is a 2 percentage point increase — but a 50% percent change ((6−4)÷4). Financial news mixes these up constantly; now you will spot it.

Forgetting that increases and decreases are not symmetric

A 50% increase followed by a 50% decrease does not bring you back to start. $100 → $150 (up 50%) → $75 (down 50%). To undo a 50% gain you need a 33.3% loss. This asymmetry trips up investors and shoppers alike.

Percent change from zero

You cannot calculate percent change when the old value is zero — the formula requires dividing by zero, which is undefined. Going from 0 sales to 10 sales is simply “10 new sales,” not any percent.

Quick Percent Change Shortcuts

For a 10% increase: multiply by 1.1. A $60 bill with a 10% tip is $60 × 1.1 = $66.

For a 20% discount: multiply by 0.8. A $75 jacket at 20% off is $75 × 0.8 = $60.

For repeated changes: multiply the factors. Two consecutive 10% raises equal 1.1 × 1.1 = 1.21, a 21% total increase — not 20%.

Mental math trick: 1% of any number is just the number with the decimal moved two places left. Build any percentage from there: 15% of $200 is (1% = $2) × 15 = $30.

These shortcuts come in handy for electrical load math and other everyday calculations where you need a fast, reliable answer.

More worked examples: test scores, salaries, and investments

Test scores: you score 72 on the first exam and 90 on the second. Percent change = ((90 − 72) ÷ 72) × 100 = (18 ÷ 72) × 100 = 25% improvement.

Salary raise: your pay goes from $52,000 to $55,000. Percent change = ((55,000 − 52,000) ÷ 52,000) × 100 = (3,000 ÷ 52,000) × 100 = 5.77% raise.

Investment loss: a $5,000 portfolio drops to $4,200. Percent change = ((4,200 − 5,000) ÷ 5,000) × 100 = (−800 ÷ 5,000) × 100 = −16%, a 16% loss.

Population growth: a town grows from 8,000 to 9,600 residents. Percent change = ((9,600 − 8,000) ÷ 8,000) × 100 = 20% growth.

Reverse-engineering discounts: saw a “was $80, now $60” tag? The discount is ((60 − 80) ÷ 80) × 100 = −25%, so 25% off. Doing this in the aisle tells you instantly whether the “huge sale” is actually huge.

Tip for chained changes: when a value changes twice, compute each step separately against its own starting value. A store price that rises 10% then falls 10% does not return to the original — $100 becomes $110, then $99. Percent change always re-baselines, which is exactly why the formula divides by the old value each time. Master these patterns, and percent change stops being a formula you look up and becomes mental math you simply do. For more everyday math, our guide to calculating voltage drop walks through another practical formula step by step.

Frequently Asked Questions

What is the difference between percent change and percent difference?

Percent change measures movement from an old value to a new value (baseline = old value). Percent difference compares two values with neither as the baseline, dividing by their average instead. Use percent change for “before and after” scenarios like prices and scores.

How do I calculate percent change in Excel or Google Sheets?

If the old value is in cell A1 and the new value in B1, enter =(B1-A1)/A1 and format the cell as a percentage. That is the entire formula — no special functions needed.

Can percent change be more than 100%?

Absolutely. If a stock goes from $10 to $35, that is a 250% increase. Percent change has no upper limit for increases. Decreases, however, cannot go below −100% (that would mean the value went negative).

How do I find the original value from a percent change?

Work backward: Original = New ÷ (1 + rate). If a $132 price reflects a 10% increase, the original was $132 ÷ 1.10 = $120. For a decrease, use (1 − rate): a $90 sale price after 25% off means the original was $90 ÷ 0.75 = $120.