Practical guides, how-tos and comparisons to get the most out of our free online tools.
One high water and the 12 h 25 min lunar interval give you every high and low for days. The rule of twelfths then tells you how much water has moved at any point in between — and both stop being reliable at exactly the same place.
Lena Hoffmann · 6 min read
343 m/s in air at 20 °C, 1,481 in water, 5,960 in steel and 12,000 in diamond. Steel is 6,500 times denser than air and carries sound only 17 times faster — density slows sound down.
Lena Hoffmann · 4 min read
A 10 mm² steel bar 2 m long stretches 1 mm under 1,000 N: 200 GPa. The same bar in aluminium stretches 2.86 mm and in softwood 20 mm. Heat treatment changes none of it.
Marco Bianchi · 3 min read
A 60 kg person on one square centimetre of heel exerts 5.89 MPa. A five-tonne elephant on four feet of 0.1 m² each exerts 123 kPa. Same physics, opposite areas.
Marco Bianchi · 4 min read
Weigh it, sink it in water, divide. 340 g displacing 40 cm³ is 8.5 g/cm³ and brass; 272 g in the same 40 cm³ is 6.8 and a zinc casting wearing brass plate.
Marco Bianchi · 4 min read
Two kilos of water need 83.72 kJ for ten degrees. The same two kilos of aluminium need 18, and of steel 9. That single number explains kettles, radiators and coastal weather.
Lena Hoffmann · 4 min read
On $52,000 a year, a fortnightly cheque is $2,000 and a twice-monthly one is $2,166.67. The second looks 8.33 % better and pays exactly the same — because there are 26 of the first and 24 of the second.
Camille Laurent · 3 min read
Eight points of excess return over a beta of 1.2 gives 6.67. Change the beta to 0.6 and the same portfolio scores 13.33 — the number moves entirely on an estimate.
Camille Laurent · 3 min read
$500,000 of operating cash on $2m of sales is a 25 % cash margin against a 15 % net margin — ten points of comfort. The same company with $100,000 of cash reads 5 % against 15 %, and that is ten points of warning.
Camille Laurent · 3 min read
$8,000 of wages on $25,000 of revenue is 32 %. Add $1,800 of employer contributions and the same week reads 39.2 % — a seven-point move with no change in staffing.
Camille Laurent · 3 min read
A $24,000 van with a $4,000 residual over five years is $4,000 a year of expense and not one dollar of payment. Change the residual to zero and the charge becomes $4,800.
Camille Laurent · 3 min read
Push with 50 N over 4 m and you have done 200 joules. Do it in two seconds and that is 100 watts; in twenty, 10 watts — the same work at a tenth of the power.
Marco Bianchi · 4 min read