Percent Change From Zero & Negative Numbers — The Right Formula

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.

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Percent 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.

Frequently 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.