What share of B is A?

Share = (A / B) × 100. 25 of 200 is 12.5%. The 'X out of Y in %' mode renders this as a donut with the percent in the centre. If B is zero, the question is mathematically undefined - the calculator hides the donut and explains why instead of returning a misleading 0.

Do +10% and -10% cancel out?

No. 100 + 10% = 110, then 110 - 10% = 99. The combined effect is -1%. With larger swings the effect is more visible: 100 → +50% → 150 → -50% → 75. Naive +50 -50 = 0; actual -25%. The chain mode shows that with the naive sum struck through.

What does relative versus absolute change mean?

An absolute change is the difference in the unit of the values (€, kg, percentage points). A relative change is the difference in percent of the starting value. 100 → 130 is absolutely +30, relatively +30%. 5% → 7% is absolutely +2 percentage points, relatively +40%. With percentages, the absolute statement is often misread as a relative one.

Percentage calculator with percentage-point trap and asymmetric recovery

A percentage calculator isn't impressive - until it also covers the modes journalism keeps getting wrong. This one has six, with two built around the traps headlines keep getting wrong: percentage points vs percent (the +2-pp-vs-+40% trap) and asymmetric recovery (a 50% loss demands a 100% gain). Each mode has a visualisation, a formula, and a reading note.

Standard Four modes you probably know.

Headline traps Where 2 percent quickly becomes 40.

Percent X (%)

Quick pick

Base Y

Result

19% of 250 is

47.50

47.50 · 19% Rest: 202.50 · 81%

Also useful: Hourly-rate calculator →

Note: not tax or financial advice. The calculator is a math tool, not a recommendation. For tax, payroll, or investment questions, ask an accountant or financial adviser.

Runs in your browser. No network call. No account.

The two showcase modes

If you only take two modes home, take these:

Percentage points vs percent. When inflation moves from 5% to 7%, that's +2 percentage points or +40% relative. Both are correct - it depends on the question. A headline that just says "inflation up 2%" leaves the framing unspecified. In the calculator above, the toggle renders the same change in both frames: left on a 0-100% scale (absolute), right with the before-value as 100% (relative). The bar moves in both modes - but the scale jump tells you why the perception is so different.

Asymmetric recovery. After a loss, you need a larger percentage gain to get back to the original value. Stocks that drop 50% need +100% to recover. 80% loss → +400%. Not marketing language - the formula is recovery % = loss / (100 - loss) × 100. The visualisation shows a V-shaped journey curve: a short red drop on the left (the loss), a noticeably longer green climb on the right (the recovery), plus a reference ladder for 10 / 25 / 50 / 80 / 90% loss. So the headline "stock has recovered the loss" implies a multiplier, not a simple flip back.

The four standard modes

The remaining four modes are the ones you've used since school:

X % of Y. Standard multiplication: result = X / 100 × Y. 19% of 250 = 47.50. Watch out when undoing VAT: 19% VAT on 100 gives 19, but in reverse net = gross / 1.19, not net = gross - 19%.

X out of Y in %. Share of a whole: percent = X / Y × 100. 25 of 200 is 12.5%. If the whole is zero the question is undefined - the calculator hides the donut and explains why instead of returning a misleading 0.

X → Y in %. Change from value A to value B: change % = (B - A) / A × 100. 100 → 130 = +30%. 80 → 60 = -25%. Both values appear as bars, coloured green or red by direction.

Chained %. Several changes in sequence. This is the one most people get wrong intuitively: percentages multiply, they don't add. +10% then -10% isn't 0%, it's -1%. The calculator shows the naive sum (struck through) alongside the actual multiplicative effect.

The most common traps

Trap	Example	Correction
Reading percentage points as percent	"Inflation up 2%" for 5 → 7	It's 2 pp or 40%, depending on the question
+X% and -X% cancelling	+50% then -50%	Actual: -25%, not 0
Loss and recovery being equal	-50% equals +50% to recover	-50% requires +100%
Subtracting VAT from gross	100 gross - 19% = 81 net	Net = 100 / 1.19 ≈ 84.03

Number formatting

The calculator formats numbers in EN notation by default: dot decimal, comma thousands, and the percent sign glued to the number (no space, English convention). The DE version under /prozent-rechner uses comma decimal, dot thousands, and a narrow no-break space before the percent sign so "47,50 %" never wraps across lines.

Cross-link: hourly rate calculator

If your calculation is a markup on an hourly rate - say, "what percent uplift on a personnel cost gives a clean billable rate?" - then the hourly rate calculator is the natural follow-up. The "X % of Y" and "X → Y" modes show a link directly underneath the calculator.

FAQ

What's the difference between percent and percentage points?

Percentage points are the absolute distance between two percentages; percent is the relative change. 5% → 7% is +2 percentage points or +40% relative. Headlines often swap these - in this example the orders of magnitude differ by 20× (in general by a factor of 100 / before-value).

How do I combine multiple percentage changes?

Not by adding. Multiply the factors (1 + percent / 100). +10% then -10% = 1.10 × 0.90 = 0.99, i.e. -1%.

Why do I need a 100% gain to recover from a 50% loss?

Because the gain is calculated from the remaining value, not the original. Formula: recovery % = loss / (100 - loss) × 100. 50% loss → 100% needed. 80% loss → 400%.

How much is X percent of Y?

X / 100 × Y. 19% of 250 = 47.50. When undoing VAT, divide by 1+rate, don't subtract.