Increase Decrease Calculator: Percent Change

This calculator works out the percentage increase or decrease between two numbers. You enter the original value and the new value, and it returns the percent change, showing whether it is an increase or a decrease. It also gives the absolute difference between the two numbers.

Formula

The percent change is calculated as:

Percent Change = ((New Value − Original Value) ÷ Original Value) × 100

• Original Value – the starting number (the base you compare against).
• New Value – the number after the change.
• Percent Change – the result, expressed as a percentage. A positive number means an increase; a negative number means a decrease.

The absolute difference is simply |New Value − Original Value|, which tells you the raw size of the change without the sign.

Worked Example

Using the default values: Original = 100, New = 80.

1. Subtract the original from the new: 80 − 100 = −20.
2. Divide by the original: −20 ÷ 100 = −0.2.
3. Multiply by 100 to get a percentage: −0.2 × 100 = −20%.

The result is −20%, meaning a 20% decrease. The absolute difference is |80 − 100| = 20.

When to Use This Calculator

Percent change is used in dozens of everyday situations. You might want to know how much a price dropped during a sale, how much your electricity bill went up compared to last month, how your investment portfolio changed over a year, or how a test score improved from one attempt to the next. The key is that you have two numbers: a starting point and an ending point. The calculator works for any pair of positive numbers, and also for negative numbers, though the interpretation becomes trickier (see below).

It is important to note that percent change is not symmetric. Going from 100 to 80 is a 20% decrease, but going from 80 back to 100 is a 25% increase. This is because the base (original value) changes. Always make sure you know which number is the original.

How to Read the Result

A positive percent change means the new value is larger than the original. A negative percent change means it is smaller. The magnitude tells you the size of the change relative to the original. For example, a 50% increase from 200 gives 300, while a 50% decrease from 200 gives 100.

If the result is 0%, the two numbers are equal. If the original value is 0, the formula divides by zero, which is undefined. In that case, the calculator cannot produce a meaningful percent change – you would need to describe the change in absolute terms instead.

Common Mistakes and Pitfalls

• Using the wrong base: The most frequent error is dividing by the new value instead of the original. Always divide by the original value.
• Confusing percentage points with percent change: If a rate goes from 10% to 15%, that is a 5 percentage point increase, but a 50% increase relative to the original 10%. The calculator gives the relative change (50%), not the absolute change in percentage points.
• Negative original values: If the original is negative (e.g., a company’s profit going from −$10,000 to −$5,000), the formula still works mathematically, but the interpretation is counterintuitive. A change from −10 to −5 gives +50%, which looks like an increase, but in absolute terms the loss shrank. Percent change with negative bases is often misleading; it is better to report the absolute difference in such cases.
• Rounding too early: If you round intermediate steps, you can get a slightly different final answer. It is best to keep full precision until the end, then round to the desired number of decimal places.

How to Choose the Right Method

This calculator is for percent change between two numbers. If you instead need to find a percentage of a number (e.g., 20% of 150), use a percentage calculator. If you need to add or subtract a percentage from a number (e.g., add 8% tax), use a percentage add/subtract calculator. If you need to compare a part to a whole (e.g., what percent of 200 is 50), use a percent of calculator. The distinction is:

• Percent change: (New − Original) ÷ Original × 100
• Percent of: (Part ÷ Whole) × 100
• Percent increase from a base: Original × (1 + Percent/100)

If you have a starting value and a percentage change, and you want the new value, use the formula: New = Original × (1 + Percent/100). For example, a 15% increase on 200 is 200 × 1.15 = 230.

Limits of the Formula

The percent change formula assumes the original value is a meaningful baseline. It works well for quantities like prices, populations, measurements, and scores. It does not work when the original value is zero or near zero, because even a tiny absolute change becomes an enormous percentage. For example, going from 1 to 2 is a 100% increase, but going from 0.1 to 0.2 is also a 100% increase – the percentage does not tell you about the absolute scale.

Also, percent change is not appropriate for comparing ratios or rates that are already percentages, unless you are explicitly interested in relative change. Always consider whether a relative change (percent) or an absolute change (difference) is more meaningful for your situation.

Frequently Asked Questions

What is the difference between percent change and percentage point change?

Percent change is a relative measure: it compares the size of the change to the original value. Percentage point change is an absolute measure: it is simply the arithmetic difference between two percentages. For example, if a tax rate goes from 10% to 15%, the percentage point change is 5 points, but the percent change is 50% (because 5 is 50% of 10).

Can I use this calculator for negative numbers?

Yes, the formula works with negative numbers, but the result can be misleading. For instance, going from −10 to −5 gives a positive 50% change, even though the value increased (became less negative). In such cases, it is often clearer to report the absolute difference or the direction of change in words.

What if the original value is zero?

If the original value is zero, the formula divides by zero, which is undefined. The calculator will not return a meaningful percent change. You should describe the change as an absolute difference instead (e.g., from 0 to 5 is an increase of 5).

How do I calculate a percentage increase or decrease without a calculator?

You can do it by hand: subtract the original from the new, divide that difference by the original, then multiply by 100. For example, from 50 to 65: (65 − 50) ÷ 50 = 15 ÷ 50 = 0.3, then × 100 = 30% increase.

Why is a 50% decrease followed by a 50% increase not back to the original?

Because the base changes. A 50% decrease from 100 gives 50. Then a 50% increase on 50 gives 75, not 100. To get back to the original, you need a 100% increase on the reduced value. This asymmetry is a common source of confusion.

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in original | Original value | - | 100 | 0
in new | New value | - | 80 | 0
out pct_change | Percent change | % | ((new - original) / original) * 100 | 2
out abs_diff | Absolute difference | - | abs(new - original) | 2