Percent Change Calculator
Percent change between two values, plus markup, discount, and percentage-difference variants
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What this calculator computes
Percent change is the standard metric for expressing how much a quantity has grown or shrunk relative to its starting value, computed as (new − old) / old × 100. The calculator handles three related but distinct percentage calculations: percent change (used for tracking how a single value moved over time, such as a stock price or a population), percent difference (used for comparing two values where neither is the obvious baseline, such as the price of two competing products), and markup or discount calculations (used for retail pricing where the cost basis is fixed and the selling price reflects a target margin). The distinction between percent change and percentage points matters in financial and statistical contexts: an interest rate moving from 5% to 6% is a 1 percentage-point increase but a 20% relative increase, and using the wrong term in a financial communication can misrepresent the magnitude by an order of magnitude. The calculator outputs both the numeric percent change and the absolute change in the original units, with sign convention indicating direction (positive for increase, negative for decrease). Common applications include tracking investment returns, retail price changes, population statistics, scientific measurement comparisons, and any context where relative change matters more than absolute change.
Calculator
The formula
Formula
percent change = (new − old) / old × 100
Worked example
When to use this calculator
Use this calculator any time you need to express a change between two values as a percentage, whether tracking a single value over time (price changes, weight loss, audience growth) or comparing two related values from different sources (cross-vendor pricing, before-and-after measurements). The percent-change form is the right choice when one value is the natural baseline and the other is the comparison point; the percent-difference form is the right choice when the two values have equal status and neither is the obvious baseline. For markup-and-discount retail work, the calculator handles cost-to-price markup (where percent markup is a function of cost) and price-to-discount markdown (where the discount is a function of original price) as separate but related cases. The calculator does not handle compound percentage growth over multiple periods, which requires the compound-growth-rate formula rather than simple percent change.
Common input mistakes
- Confusing percent change with percentage points. An interest rate moving from 5% to 6% is a 1 percentage-point increase but a 20% relative percent change. Financial-news headlines that report "interest rates up 1%" are usually wrong on the percent-vs-points distinction; the correct phrasing is "up 1 percentage point" for the additive change or "up 20%" for the relative change.
- Reversing the order of new and old in the formula. The standard formula uses (new − old) / old × 100, where dividing by the old value sets it as the baseline. Reversing to (old − new) / new flips the direction of the percent-change figure and uses the wrong baseline; a value rising from 100 to 120 is +20% by the standard formula but appears as −16.67% by the reversed formula.
Frequently asked questions
What is the formula for percent change?
Percent change equals (new value minus old value) divided by old value, times 100. The result is positive when the value has increased and negative when it has decreased. The formula uses the old value as the denominator because it sets the baseline for "change relative to where we started" — using the new value as the denominator gives a different and asymmetric result that is rarely the intended comparison.
What is the difference between percent change and percentage points?
Percent change is the relative change between two values, expressed as a fraction of the original. Percentage points are the absolute additive change between two percentages, used when the values themselves are already percentages. An interest rate rising from 5% to 6% is a 1 percentage-point increase (additive) but a 20% relative increase (because 1 / 5 × 100 = 20%). Financial reporting requires careful distinction between the two.
How do I calculate percent change for negative values?
The standard formula works directly with negative values, but the result interpretation can be confusing because the sign of the denominator affects the sign of the change. A value moving from −10 to +10 has a change of 20 absolute units, but the percent-change formula gives 20 / (−10) × 100 = −200%, which is mathematically correct but counterintuitive. For values that cross zero, the percent-change metric is often replaced by absolute change because the relative interpretation breaks down.
How do I calculate percent change over multiple periods?
For compound growth across multiple periods, use the compound-growth formula CAGR = (final / initial)^(1/n) − 1, where n is the number of periods. A value that grows from 100 to 200 over 5 years has CAGR = (200/100)^(1/5) − 1 = 0.1487, or 14.87% per year compounded. Simple percent change of 100% over the entire 5 years is correct as a total figure but does not represent the per-year growth rate that compound interest would produce.
How do I calculate markup vs discount?
Markup is the percentage added to a cost to arrive at a selling price: markup = (price − cost) / cost × 100. Discount is the percentage subtracted from an original price: discount = (original − sale) / original × 100. The two are mathematically distinct because they use different denominators, so a 50% markup and a 50% discount do not cancel out — a $100 cost marked up 50% gives $150, and that $150 discounted 50% gives $75, not the original $100.