Practical guides, how-tos and comparisons to get the most out of our free online tools.
The loan is written like a car loan and behaves like a mortgage on an asset that loses value like a car. That combination opens a negative-equity window measured in years — and the number that decides the purchase is the cost per night of use.
Marco Bianchi · 14 min read
PMI insures the lender and is billed to the borrower. On a $380,000 loan that is $228 a month at an illustrative 0.72 percent. The law gives you a request at 80 percent and an automatic exit at 78 percent — month 124 and month 135 on the schedule, but up to 86 months apart in real life.
Camille Laurent · 19 min read
The Fibonacci sequence adds each pair of terms to make the next; the ratio of neighboring terms homes in on the golden ratio φ ≈ 1.618. See how, and where the pattern turns up.
Lena Hoffmann · 4 min read
Efficiency rises with compression ratio, so why do petrol engines stop around 12:1? Because compressing a charge heats it — r to the power of gamma minus one — and above a certain temperature the unburnt end gas lights itself.
Marco Bianchi · 18 min read
The speedometer is the famous consequence, and the least expensive one. The same number sets your odometer and therefore your lease bill, your effective final drive and cruising rpm, and what the ABS believes about wheel slip.
Marco Bianchi · 13 min read
Going from 10 to 20 mpg saves six times more fuel than going from 30 to 40, over the same distance. The reason is that fuel used is the reciprocal of fuel economy — and it changes which vehicle you should replace first.
Marco Bianchi · 11 min read
Big O describes how an algorithm's work grows as input grows. Here is what O(1), O(n), O(n squared), and O(log n) mean and why the difference matters.
Daniel Okonkwo · 4 min read
Unicode assigns every character a code point; UTF-8 encodes those code points in one to four bytes. Here is how it works and why it beat the alternatives.
Daniel Okonkwo · 4 min read
We measured the coverage curve of French on 313 million words of subtitles: the top 1,000 forms account for 80.77% of running text. Then we took a normal French sentence in which 80% of the tokens are inside that top 1,000, and showed that a reader who knows every one of them learns nothing from it.
Lena Hoffmann · 17 min read
A z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.
Lena Hoffmann · 4 min read
There is a standard behind two-person, and its berth is 24 inches wide. Divide real floor plans by their occupants, compare the result with a sleeping pad, then compute how much of a quoted peak height actually exists: in a straight-sided A-frame, sitting height covers 18 per cent of the floor width.
Aisha Karim · 14 min read
Click-through rate measures how many people click after seeing your ad or link. Learn the clicks ÷ impressions × 100 formula and typical benchmarks by channel.
Daniel Okonkwo · 4 min read