A percentage question is rarely one formula. You want the cut amount, the new price, the rate behind a move, or the share one number holds of another, and the percentage calculator folds all five answers into a single box: type X and Y, pick a mode, press Enter or calculate, and the result appears with the formula that produced it, a copy button next to it.
Five modes, five formulas
The five mode buttons are percent-of, increase, decrease, what-percent, and percent-change, and the empty fields suggest their starter pairs: 25 and 200 for percent-of, 100 and 15 for both increase and decrease, 50 and 200 for what-percent, and 50 and 75 for change. The math behind them is X over 100 times Y for percent-of, X plus X times Y over 100 for increase, X minus that for decrease, X over Y times 100 for what-percent, and Y minus X over the absolute value of X times 100 for change; if your only question is that last one, the percentage change tool is the dedicated page, and it also takes a comma-separated list of values and reports each step plus the total change.
The 240 and 15 percent example
Run one price through every mode. 15 percent of 240 is 36, the cut amount. 240 decreased by 15 percent is 204, the sale price. The change from 240 to 204 is (204 minus 240) over 240 times 100, which is minus 15. And 204 is what percent of 240: 204 over 240 times 100 is 85. Each answer is one mode click away, and for a full sale-price breakdown with the savings listed separately, the discount calculator runs the same arithmetic in its own layout.
Why a 15 percent rise does not undo a 15 percent cut
Raise 204 by 15 percent and the result is 204 plus 30.6, which is 234.6, not 240, because the rise is measured against 204, the smaller number. The full undo needs 36 back on 204, about 17.65 percent, not 15. The direction also runs on everyday money: the same percent-of mode turns an 18 percent tip on a 240 bill into 43.2, and the tip calculator keeps the bill, the tip, and the split per person on one screen.
What the result line shows
The number renders to four decimals with trailing zeros trimmed, so the cut amount reads 36 and not 36.0000, and the raise reads 234.6 and not 234.6000. A blank or lettered field returns the Please enter valid numbers message, and a division with no finite answer, like what-percent with a zero second field or percent-change starting from zero, returns the Invalid calculation message. Negative percentages are accepted, so increased by minus 15 behaves like a 15 percent decrease, and switching modes clears the result while keeping both inputs.
Percent change over time
The change mode divides by the absolute value of the start, so a move from minus 100 to 100 reads as plus 200 percent, the sign carried by the difference, not the base. Over several periods the same 15 percent applied again and again compounds, so the total growth is not the sum of the individual changes, which is exactly what the CAGR calculator pulls out as one average annual rate, and what the APY to APR converter splits into a nominal rate and a compounded effective rate.
Picking the mode and reading the formula line
Start with the mode that matches the question, keep the starter pairs from the empty fields while testing, and read the formula line to see which of the five operations just ran. On the discount side, how to calculate a discount walks the sale-price example end to end, and how to calculate CAGR shows the change numbers turning into one compound rate.