Percentage Change Calculator Guide

What This Calculator Does

Choose from eleven modes: percentage increase, decrease, reverse percentage, symmetric percentage difference, part-of-total percentage, percentage value, discount, tax, tip, compound growth and cost markup. Increase, decrease, reverse and difference are placed first in the mode menu for quick access.

When to Use It

Use increase or decrease when a starting value is the reference. Use reverse when the final value and signed change are known. Use symmetric difference when neither value is the reference. For selling-price profit margin rather than cost markup, use the profit margin calculator.

Inputs Explained

Enter decimal numbers without thousands separators; comma or dot decimals and scientific notation are accepted. Inputs must be finite and within ±1 trillion. Compound periods are whole numbers from 0 to 10,000. Only displayed fields are required. Editing clears the previous result.

Increase, decrease, reverse and difference accept signed values. Increase/decrease require a nonzero starting value and retain its signed denominator. In reverse mode, −20 means a 20% decrease and +20 means a 20% increase. A −100% change has a zero multiplier and no unique original value. Changes below −100% are allowed algebraically and cross zero; they are not ordinary retail discounts.

Part-of-total requires a positive total and nonnegative part. Percentage value, tips and markup use nonnegative inputs. Discount requires a positive original price and a final price between zero and the original. Tax uses a nonnegative before-tax amount and a 0–100% rate. Compound growth requires nonnegative principal and rate.

Calculating preserves the inputs in the URL. Copy the shared link from the result to restore and calculate them on reopening. The link contains entered values.

How the Calculation Works

For original A, new value B, percentage p and periods n:

• Increase: (B−A)/A × 100%.
• Decrease or discount: (A−B)/A × 100%.
• Reverse: A = B/(1+p/100).
• Symmetric difference: |A−B|/((|A|+|B|)/2) × 100%.
• Part-of-total: part/total × 100%.
• Percentage value: total × p/100.
• Tax or tip: base × p/100; combined amount = base × (1+p/100).
• Compound growth: A × (1+p/100)ⁿ.
• Markup: cost × (1+p/100).

Symmetric difference uses the average absolute magnitude. Two zero values are defined as 0%; one zero or opposite signs gives 200%. Zero compound principal gives zero ending amount and gain, but an undefined relative growth rate is shown as a dash.

Example

• 200 falling to 150 is a 25% decrease and a decrease amount of 50.
• Final 120 with +20% change gives original 120/1.2 = 100.
• Final 80 with −20% change gives original 80/0.8 = 100.
• Symmetric difference of 100 and 120 is 20/110 × 100% ≈ 18.181818%, in either input order.
• −100 to −50 produces −50% in signed increase mode and an absolute change of +50. This is a signed-baseline convention, not a business improvement percentage.
• A before-tax amount of 100 at 13% gives tax 13 and total 113. Cost 80 with 25% markup gives price 100 and profit 20; the selling-price margin is 20%, not 25%.

How to Understand the Result

Percentage and value modes show a progress bar for percentages from 0 to 100. Nonnegative increase, decrease, discount and symmetric-difference inputs have before/after comparison bars. These visuals supplement the numeric formulas.

Change has a direction and a chosen baseline. Symmetric difference has no direction and is invariant under swapping inputs. The result includes a primary value, supporting amounts or mean magnitude, and a formula. These two percentage measures answer different questions.

Common Mistakes

Entering a positive reduction in reverse mode; calculating ordinary change from zero; interpreting a negative-baseline rate as business growth; mixing annual rates with monthly periods; confusing markup with margin.

FAQ

Why can a negative baseline show a negative increase?

Change uses (new − old) / old. The old value must be nonzero; negative baselines keep their signed denominator.

How does reverse percentage work?

Enter a signed change: +20 means a 20% increase; −20 means a 20% decrease. Original = final / (1 + change/100). A −100% change cannot be reversed.

How are zero and negative values handled in difference mode?

Difference = |A − B| / ((|A| + |B|)/2). Both zero gives 0%; opposite signs give 200%. Swapping inputs does not change the result.

Notes

Values must be finite and within ±1 trillion; compound periods are whole numbers from 0 to 10,000. This is arithmetic, with no tax rules, fees or cash-flow timing.