mph to km/h: The Conversion Factor and Mental-Math Tricks
Convert miles per hour to kilometers per hour and back with the exact factor 1.609, common speed limits in both systems, and quick tricks you can do in your head.
Daniel Okonkwo · 3 min read
Guides & tutorials
Practical guides, how-tos and comparisons to get the most out of our free online tools.
June 17, 2025
June 16, 2025
Splitting People Into Fair Groups: Random and Fair Are Not the Same Requirement
23 people do not divide into fours, and a uniformly random split can hand one group every strong player. Here is the remainder arithmetic, the measured cost of pure randomness, and the stratified fix.
Lena Hoffmann · 14 min read
June 13, 2025
Speed, Distance and Time: The Formula and How to Rearrange It
One triangle, three formulas. Learn speed = distance / time, rearrange it for distance or time, and keep your units consistent so the answer is right.
Marco Bianchi · 4 min read
June 12, 2025
Poker Hand Probabilities, Derived Rather Than Memorised
Every five-card poker probability is a counting argument over 2,598,960 hands, and each one fits on a single line. Here are all nine, with the check that proves them: the counts must sum to exactly C(52,5).
Lena Hoffmann · 13 min read
Dog Years to Human Years: The Real Formula (Not ×7)
The old "multiply by 7" rule is a myth. Learn the modern AVMA size-based method: dogs age fast early, then slower, and large breeds age quicker than small ones.
Marco Bianchi · 3 min read
June 11, 2025
Shuffling Is Harder Than It Looks: A Million Runs of the One-Line Shuffle
The shuffle everyone writes — sorting with a random comparator — is biased, and not slightly. A million measured runs show eight of the twenty-four orderings turning up twice as often as the other sixteen.
Lena Hoffmann · 13 min read
June 10, 2025
Stacked Discounts Do Not Add Up
Twenty percent off and then a further ten percent off is not thirty percent off — it is twenty-eight, because the second discount applies to the already-reduced price. The general rule, the cases where order matters, and how sales tax changes the answer.
Lena Hoffmann · 13 min read
June 9, 2025
Percentage Points Are Not Percent
Moving from 4% to 5% is a rise of one percentage point and a rise of twenty-five percent. Both statements are true, which is exactly why the ambiguity is so easy to exploit — and why basis points exist.
Lena Hoffmann · 14 min read
June 6, 2025
Leap Years: The Rule, the Exception, and the Exception to the Exception
Divisible by four, except centuries, except centuries divisible by four hundred. The three-line rule exists because the tropical year is not 365.25 days, and the arithmetic behind it explains ten deleted days in 1582 and a calendar that repeats exactly every 400 years.
Lena Hoffmann · 15 min read
Date Arithmetic Is Harder Than It Looks
"One month later" has no single correct answer, and every date library has had to pick one. Month addition is neither associative nor invertible, a day is not always 24 hours, and age is not days divided by 365.25.
Lena Hoffmann · 15 min read
June 5, 2025
Annuities: What You Are Actually Buying
An annuity's price is a present value over a probability-weighted term. On a stated mortality at 4 percent, $100,000 at 65 buys $7,492 a year — 4.00 points of interest, 1.78 of returned capital and 1.71 of mortality credit.
Camille Laurent · 14 min read
June 4, 2025
Dividend Reinvestment: What Actually Drives the Difference
Reinvesting a 3 percent yield for 30 years turns 100 shares into 242.7 and multiplies the final position by exactly that factor: $32,434 becomes $78,726. Tax at 30 percent on each dividend costs $18,223 of it — nearly two and a half times the tax actually paid.
Camille Laurent · 12 min read