Calculator tools

The arithmetic here is not hard, which is precisely why it goes wrong. Percentage change and percentage difference are not the same calculation and answer different questions. A "20% discount then 20% off" is not 40%. Return on investment quoted without a time period cannot be compared to anything. Compound growth is the one people underestimate most, because the intuition is linear and the maths is not.

So each calculator shows the formula and the inputs it used, not just a number. That matters when you have to defend the figure to someone else, or when you come back a week later and cannot remember whether the rate you entered was annual or monthly.

Three percentage questions that look the same

"What is 15% of 80", "80 is what percent of 120" and "what is the change from 80 to 92" are three different calculations, and the reason percentage mistakes are so common is that all three get called "working out the percentage". The percentage calculator separates them into labelled modes so you choose the question before you type the numbers. The one that catches people most is percentage change, because it has a direction: going from 80 to 100 is a 25% increase, but going from 100 to 80 is a 20% decrease, not 25%. The base is always the value you started from.

Stacked percentages are the other trap. Two successive 20% discounts multiply rather than add — 0.8 × 0.8 is 0.64, so the customer pays 64% of the original, a 36% discount and not 40%. The same asymmetry means a stock that falls 50% needs to rise 100% to recover. When a figure has to be reversed, work back from the final value, not the percentage.

What a return figure actually says

Return on investment is a ratio: what you got back over what you put in, minus one. On its own it says nothing about time. A 30% return over six months and a 30% return over six years are very different outcomes wearing the same number, which is why the ROI calculator also shows an annualised rate when you give it a period. That annualised figure is what you can compare across investments — and it is also the one most often left off a sales page, for the same reason.

The calculator treats all cash in and cash out as happening at the start and end. Real investments have contributions and withdrawals along the way, and for those the honest measure is an internal rate of return, which needs every dated cash flow and is outside what a single-page tool should pretend to do.

Compound growth and what it leaves out

The compound interest calculator projects a starting sum and optional regular contributions forward at a fixed rate compounded at a chosen frequency, and shows the split between what you contributed and what growth added. The interesting output is not the final number but the shape of the curve: growth in the last third of a long horizon usually exceeds everything before it, which is the whole case for starting early and the whole reason a projection is so sensitive to the rate you typed.

Two things these tools deliberately do not do: model fees and taxes, and predict the future. A compound interest projection is arithmetic on the assumptions you typed, not a forecast — real outcomes move with fees, inflation and risk that no calculator on a website knows about. A 1% annual fee on a 7% projection does not cost you 1% of the result; over thirty years it costs closer to a quarter of it. Use these tools to check a number, then check the number that matters with someone qualified.