Percent Change Calculator

Welcome to HowToChange.com's free online tool to calculate percentage change. Enter your old and new values to see how much something has increased or decreased as a percentage. Supports numbers and time formats like hh:mm, mm:ss, or hh:mm:ss.

What is Percentage Change?

Percentage change measures how much a value has increased or decreased relative to its original (old) value. It's useful for tracking changes in prices, weights, times, or any measurable quantity.

Key Points:

  • Positive result: Increase
  • Negative result: Decrease
  • Order matters – changing from old to new is not the same as new to old.
  • We use the absolute value of the old value to handle negative numbers correctly.

Percentage Change Formula

\[ \text{Percentage Change} = \left( \frac{V_2 - V_1}{|V_1|} \right) \times 100 \]

Where:

  • V₁ = Old/Initial Value
  • V₂ = New/Final Value
  • |V₁| = Absolute value of V₁ (always positive)

Step-by-Step Examples

Example 1: From 3.50 to 2.625

Change = 2.625 - 3.50 = -0.875
|V₁| = 3.50
Fraction = -0.875 / 3.50 = -0.25
Percentage = -0.25 × 100 = -25%
Result: 25% decrease

Reverse (from 2.625 to 3.50): 33.33% increase

Example 2: From -25 to 25

Change = 25 - (-25) = 50
|V₁| = 25
Fraction = 50 / 25 = 2
Percentage = 2 × 100 = 200%
Result: 200% increase

Example 3: From -25 to -50

Change = -50 - (-25) = -25
|V₁| = 25
Fraction = -25 / 25 = -1
Percentage = -1 × 100 = -100%
Result: 100% decrease

Notes

This calculator does not reverse-solve (e.g., find new value from percent). For time values, we convert to seconds for accurate calculation. If you need improvements, let us know!

Frequently Asked Questions (FAQs)

What is percentage change?

Percentage change shows how much a value has increased or decreased compared to its original value, expressed as a percentage. Positive result means increase, negative means decrease.

Why use |V₁| (absolute value) in the formula?

To correctly handle negative old values (e.g., from -25 to 25 is 200% increase). Without absolute value, the direction can be misleading.

Does it support time formats like hh:mm:ss?

Yes! Enter time as hh:mm:ss, mm:ss, or hh:mm. It converts everything to seconds internally for accurate percentage calculation.

What happens if old value (V₁) is zero?

Percentage change is undefined (can't divide by zero). The tool will show an error message. In real scenarios, avoid calculating % change from zero.

Percentage change vs percentage difference – what's the difference?

Percentage change uses the old value as base (has direction: increase/decrease). Percentage difference uses average of both values (no direction, symmetric).

Why is reverse percentage different?

Because the base value changes. E.g., 25% increase on 100 = 125, but to go back to 100 needs ~20% decrease (not 25%).

Can I add multiple percentage changes directly?

No – percentages are not additive in that way. E.g., -40% then +60% is not +20%. Apply each change sequentially on the updated value.

Is this accurate for stock prices or finance?

Yes, it uses the standard formula used in finance and statistics. It handles negative values correctly for losses/gains.