Practical guides, how-tos and comparisons to get the most out of our free online tools.
The nth most common word appears about 1/n as often as the first. We counted six public-domain books, printed rank × frequency, fitted log frequency against log rank, and got slopes between -1.02 and -1.08 in all six languages — plus the two places the law breaks.
Daniel Okonkwo · 14 min read
The index quoted in the news is almost always a price index. At 5 percent price growth and a 2.5 percent reinvested yield, 30 years turn $10,000 into $43,219 on price and $90,656 on total return — the price measure misses 58.8 percent of the gain.
Camille Laurent · 13 min read
Taxable-equivalent yield = tax-free yield ÷ (1 − marginal rate). A 3.00 percent tax-free yield is worth 3.85 percent at a 22 percent marginal rate and 5.07 percent at 40.8 percent. The trap is that it is the marginal rate, surtaxes and social levies included — leaving them out costs 0.85 points of yield.
Camille Laurent · 15 min read
Why some years have a February 29, how the divisible-by-4, -100 and -400 rules combine, and how to check any year quickly.
Lena Hoffmann · 3 min read
Two reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.
Lena Hoffmann · 4 min read
camelCase, snake_case, PascalCase, and kebab-case explained: what each looks like, where it is the convention, and how to choose one consistently.
Daniel Okonkwo · 3 min read
Count the days until any future date, understand inclusive vs. exclusive counting, and build an accurate countdown you can trust.
Lena Hoffmann · 4 min read
A cat's first two years equal about 24 human years, then add roughly 4 per year. Learn the AAHA-backed method and see life-stage examples for kittens to seniors.
Marco Bianchi · 3 min read
Convert milliliters to cups for cooking, with the key figure 1 US cup ≈ 237 mL, plus how the US cup, the metric cup, and the UK cup differ — and a ready-to-use table.
Daniel Okonkwo · 3 min read
A practical guide to turning a JSON array of objects into a clean CSV file, including how to flatten nested fields and handle the tricky edge cases.
Daniel Okonkwo · 4 min read
Three percentages that look alike but answer different questions. Learn the formula for each, when to use it, and why they give different numbers.
Lena Hoffmann · 3 min read
A knockout bracket halves its field every round, so it only closes on a power of two. The bye count, the round count, the seed order and the total number of matches all follow from that one fact — and each is a one-line derivation.
Lena Hoffmann · 14 min read