Math

Percentage Change Calculator

What this does

Compute the signed percentage increase or decrease between two values, with the absolute difference and multiplier shown alongside.

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Calculator inputs

How to use it

Using the percentage change calculator

  1. 01

    Enter the starting value

    This is the base the percentage is measured against.

  2. 02

    Enter the ending value

    Any order works numerically but keep chronological order for a meaningful sign.

  3. 03

    Read change plus context

    Signed percent up front; absolute difference and the ×-multiplier underneath.

Good to know

Why the denominator is the start, not the average

Convention defines change relative to where you began. Stock up 10% then down 10% does not return to flat; it lands at 99% of the original; because the second move divided by a smaller base. Knowing this prevents the most common portfolio-math mistake.

Zero starts break percentages

From 0 to anything is infinite growth by this formula, so the calculator refuses the input and says why. When a metric starts at zero (new users, new revenue), report absolute gains or use the ending level directly instead.

Pair the percent with the absolute gap

A 200% jump on a tiny base can matter less than a 3% move on a huge one. The rows show the raw difference precisely so headlines never outrun reality.

How it's calculated

The math behind this calculator

% change = (to − from) / |from| × 100

Subtract the start from the end, divide by the starting value, and multiply by one hundred. The sign carries meaning automatically; positive means growth, negative means decline; and a direction row spells out “increase” or “decrease” so nobody misreads a minus sign.

Assumptions & limitations

  • The starting value must be non-zero; change from zero is undefined.
  • Signs are preserved: negative results mean decreases.
  • Absolute difference is reported separately because percent alone hides scale.

Worked example

Growing from 80 to 100 is a 25% increase; the ending value is 1.25× the starting one.

FAQ

Frequently asked questions

Is a negative result bad?
It simply means the value decreased; whether that is good depends on the metric; falling costs are welcome declines.
What if the starting value is zero?
Percentage change is mathematically undefined from zero, so the calculator explains the issue rather than returning infinity.
Does reversing the order just flip the sign?
No; magnitude changes too: +25% forward becomes −20% backward, since the base differs.

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