571 in this format. Showing the 48 most recent.
120 ml at 1:1 is 60 and 60; at 1:2 it is 40 and 80. The developer's share goes from half the mix to two thirds, and so does the peroxide that does the work.
Antonio Delgado · 4 min read
6,220 M⁻¹cm⁻¹ at 100 µM through 1 cm gives A = 0.622, and 23.9 % of the light emerges. Double the path length and A doubles to 1.244 — the scale is logarithmic, and that is where it breaks.
Lena Hoffmann · 4 min read
Fifty grams of salt in five litres is 0.171 mol/kg and buys +0.175 °C. Reaching a full degree would take 285 grams — most of a box.
Marco Bianchi · 3 min read
0.15 M of a salt that splits in two and 0.30 M of one that does not give the identical 7.64 atmospheres. Only the particle count reaches the membrane.
Sofia Nunes · 3 min read
Equal amounts of a weak acid and its base give pH = pKa exactly, at any concentration. Blood runs the same equation at a 20:1 ratio and lands on 7.40.
Sofia Nunes · 3 min read
24.80 mL of 0.1 M titrant into 25.00 mL of analyte gives 0.0992 M — or 0.0496 M if the analyte releases two protons. The stoichiometry is typed, not measured.
Lena Hoffmann · 3 min read
A 28 cm latex balloon nets 14 g of lift, so a kilogram takes 72 of them. At 2,000 metres the same balloon lifts 21 % less and you need 91.
Antonio Delgado · 3 min read
Ten items in three containers force four into one of them. 367 people force a shared birthday. Neither statement tells you which container or which pair.
Lena Hoffmann · 3 min read
A 50 mm lens at f/8 gives 10.47 m — or 15.68 m if you tighten the circle of confusion from 0.03 to 0.02 mm. Both settings are defensible and they differ by half.
Antonio Delgado · 4 min read
18 shots, 8 free throws and 3 turnovers in 36 minutes gives 29.3 % usage. Five players sharing a team's whole box score get exactly 20 % each — the number is a share, not a skill.
Aisha Karim · 4 min read
Four hours a day is 28 a week and 1,460 a year — 60.8 full days. Three hours is 45.6 days and seven is 106.5. The conversion is arithmetic; what it means is not.
Sofia Nunes · 3 min read
17 mod 5 is 2 everywhere. −17 mod 5 is −2 in JavaScript, C and Java, and 3 in Python, Ruby and a spreadsheet. Both are right, and the difference is a real bug.
Daniel Okonkwo · 3 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
Two 500 N/m springs end to end give 250 N/m; side by side they give 1,000. Under the same 50 N load that is 0.2 m of travel against 0.05 m, and 5 joules stored against 1.25.
Daniel Okonkwo · 4 min read
A one-metre pendulum swings in 2.0061 seconds, not 2. Getting to exactly two takes 0.994 m — and quadrupling the length only doubles the period.
Lena Hoffmann · 3 min read
A 1,500 kg car on a 50-metre bend needs 5,880 N of sideways force at 14 m/s and 23,520 N at 28. Halving the radius instead only doubles it.
Marco Bianchi · 4 min read
A 1,500 kg car at 14 m/s carries 21,000 kg·m/s of momentum and 147,000 joules. At 28 m/s the momentum is 42,000 and the energy 588,000 — two very different accounts of the same doubling.
Lena Hoffmann · 3 min read
Reaching 27 m/s from rest in ten seconds is 2.7 m/s². Stopping from the same speed in three seconds is −9 m/s² — a third of gravity against nine tenths of it.
Lena Hoffmann · 4 min read
Parallel sides of 8 and 5 with a height of 4 give an area of 26 — the average width times the height. Make the two sides equal and it is a rectangle; shrink one to nothing and it is a triangle.
Lena Hoffmann · 4 min read
A 20 by 16 foot deck is 320 square feet of floor. Add 40 feet of railing and four steps and the surface to cover is 544 — the parts nobody counts are 41 % of the job.
Marco Bianchi · 4 min read
A 12 by 7.5 metre lawn is 90 m², or 94.5 with a 5 % allowance. That allowance adds eighteen slabs, five rolls — and no pallets at all, because three cover both.
Marco Bianchi · 4 min read
A patch 12 ft by 10 ft at 4 in deep is 40 cubic feet, which is 1.48 cubic yards — dividing by 27, not by 3. The same trap in metric is dividing by 100 where a million belongs.
Marco Bianchi · 3 min read
Radius 5, height 10: the cone holds 261.8 and the cylinder around it holds 785.4. The ratio is exactly a third, and it holds for any base shape at all.
Lena Hoffmann · 4 min read
A cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.
Marco Bianchi · 3 min read
30 wins in 50 games is a win rate of 60 %. The 95 % interval around it runs from 46.4 % to 73.6 % — twenty-seven points wide, and wide enough to contain a losing record.
Aisha Karim · 3 min read
Five incomes of 10,000 to 90,000 give a Gini of 0.38. Divide every one of them by ten and the answer is still 0.38 — the measure sees proportions and nothing else.
Camille Laurent · 3 min read
With an average of five events per interval, exactly three occur 14.0 % of the time, none at all 0.7 %, and ten or more 3.2 % — about once every 31 intervals. The distribution has one parameter, and it sets both the mean and the variance.
Daniel Okonkwo · 4 min read
The harmonic mean of 40 and 60 is 48, not 50, because the slower leg takes longer and therefore counts for more. For 1, 2 and 4 it is 1.714 against an arithmetic mean of 2.33.
Lena Hoffmann · 3 min read
For 2, 5, 7, 8, 10, 13, 18, 21, 25, 30 the range is 28, the standard deviation 9.24 and the IQR 13. Replace the last value with 300 and only the IQR survives unchanged.
Lena Hoffmann · 3 min read
At 120 BPM a quarter note lasts 500 ms, an eighth 250 and a dotted eighth 375. One division produces the whole table, and the dotted eighth is the one that changed how delay pedals are used.
Antonio Delgado · 3 min read
Three semitones above A4 is 440 × 2^(3/12) = 523.25 Hz. The twelfth root of two makes every interval slightly wrong except the octave, and that compromise is what lets a keyboard play in any key.
Antonio Delgado · 3 min read
The three digits are two figures and a count of zeros, in picofarads: 104 is 100 nF and 473 is 47 nF. The trap is 220, which is 22 pF — while a 220 pF part is marked 221.
Daniel Okonkwo · 4 min read
10 mH with 100 µF resonates at 159.2 Hz. Double the capacitance and it falls to 112.5 Hz; to halve the frequency you have to quadruple a component, because both sit under a square root.
Daniel Okonkwo · 3 min read
1,000 Ω with 100 µF gives a time constant of 0.1 s. The capacitor is 63 % charged at that point, 95 % after three constants and 99.3 % after five — the last of which is the number that matters.
Daniel Okonkwo · 3 min read
100, 220 and 330 µF in series come to 56.9 µF — less than the smallest. Put 100 µF and 1 µF in series and the total is 0.99 µF, while the small one carries 99 % of the voltage.
Daniel Okonkwo · 3 min read
25 million of revenue across 250 people is 100,000 each. Move fifty of them to a supplier and the same revenue reads 125,000 — a 25 % improvement in a productivity measure, with the same work being done.
Daniel Okonkwo · 3 min read
500,000 of liabilities against 1,200,000 of assets is 41.7 % debt, 58.3 % equity and a debt-to-equity of 0.71. The third one runs to infinity as the equity vanishes; the first cannot pass 100 %.
Camille Laurent · 3 min read
5 million of operating profit on 20 million of capital employed is a 25 % return. Against a cost of capital of 8 % that is a spread of 17 points; at 6 % it would be a spread of −2, and every extra euro invested would destroy value.
Camille Laurent · 4 min read