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Practical guides, how-tos and comparisons to get the most out of our free online tools.

September 22, 2026
Explainer · Business

The Count Says 48,200 and the Books Say 50,000

A gap of 1,800 is a shrinkage rate of 3.6 %. The percentage is the number that travels; the absolute figure is the one that pays for the fix.

Camille Laurent · 3 min read

Explainer · Business

Four Points of Service Level Cost 41 % More Stock

Going from a 95 % service level to 99 % raises the z-score from 1.645 to 2.326 and the safety stock from 346 units to 488. The last few points of availability are the expensive ones.

Lena Hoffmann · 3 min read

September 21, 2026
Explainer · Finance

Two Accepted Models, Two Points Apart on the Same Company

CAPM and the dividend growth model both compute the cost of equity. On one set of inputs they give 9 % and 7 % — and the choice between them decides a valuation more than any figure inside either.

Camille Laurent · 3 min read

Explainer · Finance

One Point of Discount Rate Moves a Perpetuity by a Quarter

A payment of 1,000 a year is worth 20,000 at a 5 % discount rate and 25,000 at 4 %. The formula is a single division, and that is exactly why the input matters more than the arithmetic.

Camille Laurent · 3 min read

September 18, 2026
Explainer · Everyday

Water Does Not Always Boil at 212 °F

Boiling point follows air pressure, so it falls about one degree Fahrenheit every 550 feet. In Mexico City water boils at 198 °F, in Denver at 202 °F, and on Everest at 157 °F — which is why altitude changes cooking times.

Lena Hoffmann · 4 min read

Explainer · Everyday

Printing A4 on Letter Shrinks It to 94 %

A4 and US Letter differ by 5.9 mm one way and 17.6 mm the other, so "fit to page" scales the whole document to 94 %. Ten-point type becomes 9.4, and a plan drawn to scale is wrong by six per cent.

Marco Bianchi · 4 min read