How this instrument works
Nearly every percentage problem is one of three questions wearing different clothes. "What is 15% of 240?" scales a quantity. "36 is what percent of 240?" compares a part to a whole. "What changed between 200 and 260?" measures movement relative to a starting point. People reach for the wrong formula not because the math is hard but because the question is ambiguous — so this instrument makes you choose the question first.
Each mode shows its own formula and substitutes your numbers into it, line by line. If you have ever typed numbers into a percentage calculator and quietly wondered which direction it divided, the working block below the readout is the cure.
- Choose the question on the SOLVE FOR dial: X% of Y, X as % of Y, or the change from X to Y.
- Type your two numbers — the labels adjust to the chosen question.
- Read the result and, right under it, the exact arithmetic that produced it.
Worked example — the restaurant bill
A dinner bill lands at $240 and you want to tip 15%. Mode one: 240 × 15 ⁄ 100 = $36. That is the whole calculation, and the working line prints it exactly that way.
Now reverse it: the card statement later shows you actually left $36 on $240 — mode two confirms 36 ⁄ 240 × 100 = 15%. And if next month the same dinner costs $260, mode three reports the damage: (260 − 200) ⁄ 200 × 100 = a 30% rise from what you used to pay at the old $200 price.
Questions
Why is the change from 200 to 260 +30%, but from 260 to 200 only −23%?
Because percent change is measured against the starting value, and the two directions start from different places. Up from 200, the 60-unit move is 60⁄200 = 30%. Down from 260, the same 60 units is 60⁄260 = 23.1%. This asymmetry is why a 50% loss needs a 100% gain to break even.
What is the difference between percent and percentage points?
If an interest rate moves from 4% to 6%, it rose two percentage points — but the rise itself is 50% in relative terms (2 is half of 4). News reports mix these constantly. This instrument computes relative percent; when comparing two rates, subtract them yourself for points.
How do I find the price before a discount?
Use mode two backwards. If a jacket costs $68 after a 15% discount, then $68 is 85% of the original. Ask: 68 is 85% of what? Rearranged, 68 ⁄ 85 × 100 = $80. A dedicated reverse-percentage instrument is on the board; until then this dial covers it in two steps.
Why does mode two refuse to compute when Y is zero?
"X as a percent of zero" divides by zero, which has no defined answer — no matter what some calculators display. The instrument blanks the readout and says why rather than inventing a figure; that rule holds across every sheet on this site.