Guides
Every tool here calculates something specific. These pieces explain the arithmetic underneath it — worked through with real numbers, including the mistakes that are easy to make and expensive to keep.
- Pricing & Profit · 5 min readMarkup vs margin: the difference that costs money at discount timeA 50% markup is a 33.3% margin, not 50%. Here is the conversion, and the arithmetic that shows why discounting hurts more than most people expect.Read the guide
- Everyday Arithmetic · 5 min readPercentage change: five traps that make correct arithmetic look wrongUp 20% then down 20% does not return you to the start, and a zero baseline has no percentage change at all. Here are the five places percentages mislead.Read the guide
- Personal & Business Finance · 5 min readCompound interest: the three assumptions that change the answer mostOne headline rate, different answers: compounding frequency, contribution timing and nominal versus effective all change the result.Read the guide
- Lending & Debt · 5 min readWhere your loan interest actually goes in year oneOn a 30-year loan at 6%, 83% of year one's payments is interest and the balance barely moves. The arithmetic, and what it means for overpaying.Read the guide
- Advertising & Monetisation · 5 min readCPM vs RPM: why your ad revenue never matches the CPM you were quotedCPM and RPM are calculated from opposite ends of the same ad transaction. Here is exactly which divisor each one uses, and why the gap is not an error.Read the guide
- Everyday Arithmetic · 5 min readSplitting a bill so the cents add upA $115 bill split three ways does not divide. The extra cent must land somewhere, and deciding where in advance avoids the argument.Read the guide
- Marketing Analytics · 5 min readFour ways UTM tracking silently breaks, and the naming rules that prevent itCampaign tracking rarely fails loudly. It splits one campaign into three rows and credits the wrong source. The four causes, and the rules that stop them.Read the guide
- Social Media · 5 min readEngagement rate vs reach: the number your client is actually asking aboutThere are three engagement rates and they can differ twenty-fold. Which one you quote decides whether the report reads as success or failure.Read the guide
- Content & SEO · 5 min readKeyword density is not a ranking factor: what to check insteadThe advice to hit a keyword density target is decades out of date. What a word count is genuinely useful for — and how to use it without padding.Read the guide
- Agency Operations · 5 min readAgency ROI: deciding whether a retainer is actually worth takingA retainer sells capacity, not work. The arithmetic that turns a headline figure into an honest hourly rate — including the hours nobody counts.Read the guide
- AI & API Costs · 5 min readHow LLM API pricing actually works, and why your bill does not match your estimateTokens are billed twice — in and out — and a chat resends its whole history every turn. Where real API bills actually come from.Read the guide
- Marketing · 5 min readYouTube CTR: why the thumbnail decides the clickYour thumbnail and title are the only two things a viewer sees before deciding. Here is what actually moves CTR, and which numbers are a myth.Read the guide
- Dates & Time · 5 min readDate arithmetic: counting days, working days and deadlines without getting it wrongTwo people can count the days between the same dates and disagree by three. The difference is conventions — and which ones your contract assumes.Read the guide
- Dates & Time · 5 min readHow old are you, exactly: age, birthdays and eligibility datesAge counts completed years, not days divided by 365. That decides every threshold — and a 29 February birthday makes it a one-day question.Read the guide
- Study & Assessment · 5 min readWeighted grades: how to work out what you actually needAveraging your percentages is wrong when assessments carry different weights. The arithmetic that answers the question you actually asked.Read the guide
- Words & Wordplay · 5 min readHow to solve an anagram without staring at itAnagrams are solved by method, not insight: work the structure in a fixed order — endings, vowels, digraphs — and let a dictionary search.Read the guide
- Writing & Code · 6 min readText case conventions: which one to use, and where each one breaksTitle case, camelCase, snake_case and url-slug transform the same text differently. What each is for, and where a converter cannot know what you meant.Read the guide
Want a guide for something that is not here? Tell us what you are stuck on — the requests that get written up are usually the ones where the arithmetic keeps causing arguments.