Guides
The reasoning the calculators leave out.
A calculator answers one question and stops. These are the longer explanations behind them — where a formula comes from, which convention it assumes, and the specific mistakes that make an answer wrong even when the arithmetic is right.
One guide per category, each linking back to the tools it covers. Every figure quoted has been run through the same engine the calculators use.
Building & materials
- How much concrete do I need? Volume is the easy part. Which unit to order in, and how much to add on top, is where the money goes. 6 min read
- Wall area is not floor area The single mistake that runs through painting, tiling, boarding and papering — and the arithmetic that fixes it. 5 min read
- The fence post problem Decks, fences, roofs and stairs are counting problems, and they go wrong in the same handful of ways every time. 5 min read
- Buying soil and mulch by the yard Bags look cheap until you count them. Where the crossover to bulk delivery actually is, and how deep to spread. 5 min read
- Bricks, blocks and the mortar joint A brick occupies more space than a brick. That is the whole of masonry estimating, and the reason the standard sizes look so odd. 4 min read
- Bigger is not better: sizing home systems Oversizing an air conditioner makes a room cold and clammy. The same logic runs through hot water, insulation and solar. 5 min read
Money & credit
- What actually decides a mortgage payment Three numbers set the payment, and one of them does most of the work. Where the interest goes in the early years, and why overpaying is worth so much. 5 min read
- Compound interest: what actually matters Time and contributions do nearly all the work. Compounding frequency, which everybody asks about, does almost none. 5 min read
- The rate is not the cost A lower advertised rate with a fee attached is often the more expensive loan. How to compare offers that are not describing the same thing. 4 min read
- Avalanche or snowball One order costs less. The other finishes something sooner. Here is what the gap between them is actually worth. 4 min read
- What a return figure hides Charges, the order of returns, and the difference between a projection and a promise. Plus the one guaranteed return most people leave on the table. 5 min read
Health & fitness
- What BMI cannot tell you A single ratio of weight to height, invented for populations and applied to people. What it is good for, and the simpler measure that beats it. 5 min read
- Calories in, calories out — and why it is harder than that The arithmetic is simple and every number in it is an estimate. Which ones to trust, which to test, and why the timeline is always optimistic. 5 min read
- Training by numbers Heart rate zones, one-rep maxes and race predictions all rest on estimates. Knowing how rough each one is changes how you use it. 5 min read
Business & work
- Margin is not markup The same percentage means two different prices. Confusing them is the most expensive arithmetic mistake in retail, and it always goes the same way. 4 min read
- What an employee actually costs Salary is between seventy and eighty per cent of the real figure. The same gap explains why a contract rate has to look so much larger. 4 min read
Vehicles & fuel
- Why mpg lies to you A five mpg improvement is worth twelve times as much at the bottom of the range as at the top. That is not intuition failing — it is the measure being upside down. 4 min read
- What charging actually costs Where you plug in matters more than what you drive. Plus the two places an EV quietly loses energy you have paid for. 4 min read
- What a mile really costs Fuel is about a fifth of it. The rest is the part nobody writes a cheque for, which is exactly why it gets forgotten. 4 min read
- Tyre sizes and engine numbers A tyre size mixes three unit systems in six characters. Engine displacement is rounded before it reaches the badge. Both mislead in predictable ways. 4 min read
Everyday maths
- The two percentage mistakes A 20% fall does not undo a 20% rise, and percentages of different things cannot be added. Almost every percentage error is one of those two. 4 min read
- Area, perimeter and volume without the formula sheet Almost every shape formula is a rectangle with an adjustment. Once you see which adjustment, there is very little left to memorise. 4 min read
- The conversions worth memorising Six factors cover almost everything, most of them are exact by definition, and one conversion is not a multiplication at all. 4 min read
- Counting days properly A month is not thirty days, both ends may or may not count, and adding a month to 31 January has two defensible answers. 4 min read
- Helping with maths homework when the method has changed The answer is not the point — the marks are in the working. What the methods are actually teaching, and why showing a shortcut can lose marks. 5 min read