Delta percentage is calculated by subtracting the old value from the new value, dividing by the old value, and multiplying by 100. The formula looks like this: ((New Value – Old Value) / Old Value) × 100. A positive result means an increase, and a negative result means a decrease.
The Formula Step by Step
Say a product’s price went from $35 to $45.50. Here’s how to find the delta percentage:
- Step 1: Subtract the old value from the new value. $45.50 – $35 = $10.50
- Step 2: Divide that result by the old value. $10.50 / $35 = 0.30
- Step 3: Multiply by 100 to convert to a percentage. 0.30 × 100 = 30%
The price increased by 30%. If the new number were smaller than the old one, you’d get a negative result, telling you the value decreased. A drop from $35 to $28, for example, gives you (($28 – $35) / $35) × 100 = -20%.
When the Starting Value Is Negative
The standard formula breaks in certain situations. If your old value is negative, like a company reporting a loss of $100 one quarter and a profit of $50 the next, the regular formula produces misleading results because dividing by a negative number flips the sign of your answer.
One common fix is to use the absolute value of the old number in the denominator: ((New – Old) / |Old|) × 100. In the example above, that gives you (($50 – (-$100)) / 100) × 100 = 150%. This approach preserves the direction of change: a positive result still means improvement, and a negative result still means decline.
However, this fix has limits. It produces a number, but interpreting that number as a true “percentage increase” can be misleading when you’re working with losses and gains. Many financial reporting services simply don’t calculate percentage change when either period involves a net loss. They’ll display a placeholder like “N/A” or “P” (for profit) instead of forcing a number that could confuse readers.
When the Starting Value Is Zero
If your old value is zero, the formula requires dividing by zero, which is undefined. There’s no mathematically valid percentage change from zero to any other number. In practice, you’ll need to report this as an absolute change (the raw difference) rather than a percentage, or use an alternative metric that fits your context.
Percentage Change vs. Percentage Points
This distinction trips people up constantly, especially in business and policy discussions. Percentage change measures the relative shift between two numbers. Percentage points measure the simple arithmetic difference between two percentages.
Here’s the difference in action: if 81.4% of men and 85.9% of women in a group completed a certain education level, the difference is 4.5 percentage points. That’s a straightforward subtraction: 85.9 – 81.4 = 4.5. But if you wanted the percentage change between those two figures, you’d calculate ((85.9 – 81.4) / 81.4) × 100 = 5.5%. Mixing these up can dramatically overstate or understate a comparison, so it’s worth being precise about which one you mean.
Related Formulas You Might Actually Need
Percentage change isn’t always the right tool. Two similar formulas serve different purposes, and picking the wrong one skews your results.
Percent error compares a measured or estimated value against a known correct value: (|Approximate Value – Exact Value| / |Exact Value|) × 100. You’d use this in science or engineering when checking how close your measurement came to the accepted answer. The absolute value signs mean the result is always positive, since you only care about the size of the error, not its direction.
Percentage difference compares two values when neither one is the “original” or “correct” one: (|Value A – Value B| / ((Value A + Value B) / 2)) × 100. This divides by the average of both values instead of treating one as the baseline. It’s useful when comparing two independent measurements, like the output of two machines or the populations of two cities.
How to Calculate It in a Spreadsheet
In Excel or Google Sheets, the simplest approach is a cell formula. If your old value is in cell A1 and your new value is in B1, enter:
=(B1-A1)/A1
Then format the cell as a percentage (select the cell, click the % button or use Format > Number > Percent). The spreadsheet handles the “multiply by 100” part for you when you apply percentage formatting.
If you want to handle potential errors, like a zero in the old value, wrap it in an IFERROR function: =IFERROR((B1-A1)/A1, "N/A"). This returns “N/A” instead of a division error when the old value is zero.
For dashboards or reports where you want a visual indicator, Google Sheets lets you build a formula that adds an up or down arrow based on the direction of change. The core logic uses an IF statement to check whether the new value is greater than the old value, then concatenates the appropriate arrow symbol with the rounded percentage. You can pair this with conditional formatting rules to color increases green and decreases red.
Common Uses in Business
Year-over-year (YoY) growth is one of the most frequent applications of delta percentage. It compares a metric from one year to the same metric from the previous year: ((This Year – Last Year) / Last Year) × 100. Companies use it to track sales, revenue, expenses, and profit over time. The same formula works for month-over-month comparisons when you need to spot shorter-term trends or seasonal patterns.
In investing, percentage change is the standard way to express how a stock or asset has moved. If a stock went from $150 to $165, that’s a 10% gain. Framing it as a percentage rather than a dollar amount makes it easy to compare across assets with wildly different price levels.
One practical note: when you see consecutive percentage changes, they don’t simply add up. A 50% increase followed by a 50% decrease doesn’t bring you back to the original number. Starting at 100, a 50% increase takes you to 150, and a 50% decrease from 150 brings you to 75. Keep this asymmetry in mind when interpreting compounding changes over multiple periods.