Percent Change From Zero & Negative Numbers — The Right Formula
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The standard percent change formula breaks down in two common situations: when the original value is zero (division by zero) and when values are negative. These come up constantly in finance, analytics, and business reporting — and they trip up even experienced analysts.
The Standard Percent Change Formula
% Change = ((New Value - Old Value) / Old Value) × 100
This works perfectly when both values are positive and the old value is non-zero. Problems arise when old value = 0, or when one or both values are negative.
Use the Percentage Calculator for standard percent change — enter old value and new value to get the result instantly.
Percent Change When Starting From Zero
If the old value is 0, the formula produces a "divide by zero" error — technically undefined. In practice, three approaches are used:
Option 1 — Report as "N/A" or "∞": This is mathematically correct. If you had 0 sales last month and 100 this month, the percentage change is literally undefined (infinite growth). Many financial reports use "N/M" (not meaningful).
Option 2 — Use absolute change instead: Report the actual number change (0 → 100 = +100 units) rather than a percentage. This is more informative and honest.
Option 3 — Use a baseline of 1 or a small non-zero value: Some analytics tools substitute 0 with 0.001 or 1 to force a number. This is technically incorrect but sometimes necessary for charting systems that require a percentage value.
The key rule: if old value = 0, don't force a percentage. Report absolute change or flag as N/A.
Sell Custom Apparel — We Handle Printing & Free ShippingPercent Change Between Two Negative Numbers
The formula still works with negatives, but the result can be counterintuitive:
Going from -100 to -50 (the loss got smaller, which is an improvement):
- ((-50) - (-100)) / |(-100)| × 100 = 50/100 × 100 = 50% improvement
Going from -50 to -100 (the loss got bigger, which is worse):
- ((-100) - (-50)) / |(-50)| × 100 = -50/50 × 100 = -100% (worsened)
The key: Use the absolute value of the old value as the denominator when working with negatives to keep the sign of the result meaningful (positive = improvement, negative = worsening).
Negative-to-Positive and Positive-to-Negative Changes
When the sign of a value flips, standard percentage change produces misleading numbers:
Going from -10 to +10 (profit swing): ((10 - (-10)) / |(-10)|) × 100 = 200% — this is technically correct but doesn't communicate the qualitative shift from loss to profit.
Best practice: Describe the change qualitatively first, then quantify:
- "Profit swung from a $10K loss to a $10K gain (+$20K, turnaround)"
- "Customer score improved from -15 to +22 (turnaround of 37 points)"
Percentage alone is misleading when crossing zero. Context matters more than the number.
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Open Free Percentage CalculatorFrequently Asked Questions
How do you calculate percent change when the original value is zero?
You can't — dividing by zero is undefined. Options: report absolute change instead (e.g., "+50 units"), use "N/A" or "∞" in your report, or note the change qualitatively ("from 0 to X for the first time").
What is the percent change from -20 to -5?
Using absolute value of the original: ((-5) - (-20)) / |-20| × 100 = 15/20 × 100 = 75% improvement (the negative value reduced by 75%).
How do I calculate percent change in Excel when there's a zero?
Use: =IFERROR((B1-A1)/ABS(A1)*100,"N/A"). The IFERROR handles divide-by-zero. ABS(A1) uses the absolute value for negative denominators.
Brandon spent six years as a project manager where he became the team's go-to "tools guy" — always finding a free solution first. He covers generator tools and productivity utilities with a focus on real time savings.
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