Percentage change or percentage points? Choose the right calculation
A percentage result needs a base. If a price rises from 80 to 100, the increase is 20 units, but the relative increase is 25% because the base is 80. Reversing the move gives a 20% decrease, because the base is now 100. The same numerical difference can therefore produce different percentages.
Match the tool mode to the question
| Question | Inputs and mode | Result |
|---|---|---|
| What share is 30 of 120? | A=30, B=120; A as a percentage of B | 25% |
| How much is a 15% discount on 80? | A=80, B=15; B percent of A | 12 |
| How much did 80 grow to reach 100? | A=80, B=100; Percentage change | 25% |
For the discount example, 12 is the discount amount. Subtract it from 80 to obtain a final price of 68. The tool does not automatically apply tax, fees or currency rounding.
Separate changes in rates from changes in amounts
Suppose a completion rate rises from 10% to 12%. Subtracting the rates gives a rise of two percentage points. To measure relative growth, divide that two-point rise by the original rate of 10: the result is 20%. In change mode, enter 10 and 12. Reporting a “2% increase” would be ambiguous unless you explicitly mean percentage points.
Why equal increases and decreases do not cancel
Start at 100, increase by 20% to 120, then decrease the new value by 20%. The decrease is 24, leaving 96. Each step uses its own current base. To return from 120 to 100, the decrease is approximately 16.6667%, not 20%. This is useful when checking successive markdowns or interpreting a chart with relative changes.
Recover an original amount
If 68 is the amount after a 15% reduction, the original amount is 68 ÷ 0.85 = 80. Adding 15% to 68 gives 78.2, which is not the inverse. The current tool does not have a dedicated reverse-discount mode; use the formula with a general calculator instead of choosing a superficially similar mode.
Zero and negative bases need extra care
A change from zero to 10 has no finite percentage increase because the usual formula divides by zero. Describe it as an increase of 10 units. ToolDock rejects a zero base. For negative starting values, it divides the difference by the absolute original value, so -20 to -10 displays a positive 50% change. That convention may differ from a spreadsheet or domain-specific report; state the formula when comparing results.
Report the result with enough context
Include the old value, new value, period, units and whether you mean percent or percentage points. Keep full precision during intermediate calculations and round the final reported value according to the destination’s needs. The calculator uses ordinary JavaScript numbers and displays up to ten significant digits; it is not an exact-decimal accounting engine.