Understand the Math, Don't Just Punch It In
Our guides explain the formulas behind every SolvWise calculator — where they come from, when they apply, and where they break. Each guide pairs with a live calculator you can use while reading.
A calculator is only useful if you trust the number it gives you — and trust requires understanding. Every guide on this page walks through a core piece of everyday math: the amortization formula your lender applies (and the PITI components it hides), the compound interest mechanics behind the 4% rule of retirement spending, the strengths and blind spots of body-weight metrics like BMI, and the percentage and conversion math that quietly affects grocery bills, tips and DIY projects. Nothing here requires registration, and every formula is written in plain notation with a fully worked example you can reproduce by hand.
The Four Guides
Everything about monthly payments: the amortization formula, PITI components, how interest rate and term interact, what an 85% vs 90% LTV mortgage really changes, and how to sanity-check any lender's quote in under a minute.
Compound interest from first principles: why the 4% rule exists, when the Rule of 72 fails, how to project a portfolio with contributions, and the exact formulas behind each projection.
BMI, body fat (US Navy & Deurenberg methods), basal metabolic rate and daily calorie needs — what each metric measures, what it doesn't, and which ranges the WHO and medical literature actually support.
Percentages that people get wrong, tip math, unit conversions that trip up recipes and engineering, plus fast mental-math shortcuts with worked examples for each.
How These Guides Are Written
Each guide follows the same editorial discipline. First, we identify the primary source of the formula — the lender's standard amortization definition, peer-reviewed body-composition papers, or WHO reference ranges — and cite it at the bottom of the page. Second, we build the calculator directly from that formula, rounding nothing silently. Third, a worked example with realistic inputs appears inside each article so you can verify the tool's output with a pencil before you rely on it. When two methods disagree (as Deurenberg and the US Navy circumference method do), we show both and explain when each is the better choice.
The guides are reviewed on a rolling schedule — formulas, source citations and example numbers are re-checked every six months, and any correction is applied with its date visible on the page. Our methodology page documents how sources are selected and how the calculators are tested, and the editorial policy explains who writes and who reviews.
From Guide to Calculator
Reading is the fastest way to absorb the concept; using the tool is the fastest way to apply it to your own numbers. That's why every guide page embeds and links to its matching calculator — the mortgage guide pairs with the mortgage calculator, the investing guide with the compound interest calculator, the health metrics guide with the BMI calculator, and the practical math guide with the percentage calculator.
Frequently Asked Questions
Are the guides and calculators really free?
Yes. Every SolvWise calculator and guide is free to use without an account, and the site is funded by unobtrusive advertising rather than paywalls or data sales.
Can I use these guides as financial or medical advice?
No — they're educational explanations of the math, not personalized advice. For decisions with real consequences (a mortgage signature, a medical reading), use the tools to understand your numbers, then consult a qualified professional with them.
How often are the formulas re-checked?
On a rolling six-month schedule, plus immediately whenever a reader reports a discrepancy. Corrections are published with the date they were applied.
Which guide should I start with?
Pick the one that matches the decision you're facing this month. Buying or refinancing a home? Start with the mortgage guide and its amortization walkthrough. Planning retirement contributions or judging a fund's fees? The investing guide builds compound interest from first principles. Comparing a doctor's reading against published ranges? The health metrics guide maps every band to its source. Confused by a discount, a tip or a recipe conversion? The practical math guide covers exactly these cases with worked examples.
Do the guides cover the same ground as the calculators?
They're deliberately different layers. The calculators answer your numbers — type inputs, get the result and the steps that produced it. The guides answer the questions a calculator can't: why the amortization formula weights early payments toward interest, when the Rule of 72 stops being accurate, why BMI misreads muscular athletes, and which rounding habits quietly distort percentage change. Reading the guide first typically takes five minutes and makes the calculator's output self-explanatory.
Can I cite or reuse a SolvWise guide?
Yes, with attribution and a link. Teachers use the worked examples in class, and writers quote the formula explanations with their source citations. We ask only that you link to the guide rather than copying the text, so readers always see the latest reviewed version.
What Each Guide Covers in Detail
The mortgage guide opens with the monthly payment formula M = P·r(1+r)n/((1+r)n−1), defines every letter in plain English, then walks through a real $350,000 loan at 6.5% over 30 years: $2,212.24 principal and interest, $446,406 total paid of which $96,406 is interest, and why the same loan at 6.0% costs $113.81 less every month — $40,972 across the full term. It separates principal, interest, taxes and insurance (PITI), explains how extra principal payments shorten the schedule, and closes with a lender-quote checklist you can follow in minutes.
The investing guide derives compound interest step by step — $10,000 at 7% becomes $19,672 in ten years, and the same account with $200 monthly contributions reaches $54,288 — then explains the 4% rule's origin in the Trinity study, its 90%+ historical success rate over 30-year retirements, and the failure modes: sequence risk, inflation drift, and fees that compound against you at exactly the same rate gains compound for you.
The health metrics guide contrasts the four weight and energy formulas people actually encounter: BMI's CDC bands (18.5–24.9 normal) and its well-documented blind spots, the US Navy circumference method's ±3–4% accuracy for body fat, Mifflin-St Jeor for basal metabolic rate (the equation clinical dietitians default to), and how to combine all three into a sensible daily calorie target with the standard activity multipliers.
The practical math guide fixes the percentage mistakes that cost real money: why a 20% discount followed by a 20% markup does not restore the original price, how a restaurant tip splits across a shared bill, why percentage change and percentage difference are different questions, and mental shortcuts — 10% then halve it for 5%, double-and-shift for 20% — that hold for every currency.