295 guides on everyday. Showing the 48 most recent.
The arithmetic of an ordinary day: percentages, dates and durations, quantities, conversions. Short guides that show the working rather than just the answer, so the next one is a sum you do yourself.
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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
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
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
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 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
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
Sunrise, sunset and the moment the sun is highest all hang off your longitude, not off the clock on the wall. In the same legal time zone, solar noon can be an hour and three quarters apart — and that gap explains most surprises about when the sun comes up.
Lena Hoffmann · 7 min read
8 grams obtained where 10 were possible is an 80 % yield. Chain five such steps and 32.8 % of the starting material reaches the end — which is why a long synthesis is judged step by step.
Lena Hoffmann · 3 min read
One mole per kilogram of a salt that splits in two lowers water's freezing point by 3.72 °C. The same amount of something that stays whole manages 1.86 °C — exactly half.
Marco Bianchi · 3 min read
Mass percent divides by the solution, not by the solvent. Twenty-five grams into a hundred gives 125 grams of solution and 20 %, a quarter less than the number most people expect.
Lena Hoffmann · 3 min read
0.5 mol in 2 litres is 0.25 mol/L. The two litres have to be the finished solution — adding solute to two litres of water gives something else, and the label will be wrong.
Lena Hoffmann · 3 min read
2 is to 5 as 8 is to 20. Map scales, unit prices, percentages, recipe scaling and drawing enlargements are the same equation wearing five different names.
Lena Hoffmann · 3 min read
The rule of three turns 3 → 12 into 5 → 20, and that is right for anything that scales up together. For workers and days it is exactly backwards: the answer is 7.2.
Marco Bianchi · 3 min read
500 down to 350 is a fall of 150, or 30 %. When the quantity is itself a percentage, the same fall has two correct descriptions and they differ by more than a factor of ten.
Lena Hoffmann · 3 min read
Going from 50 to 75 is +50 %. Coming back from 75 to 50 is −33.3 %. The move is the same 25 units both times; the base is not.
Lena Hoffmann · 3 min read
Outcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.
Antonio Delgado · 4 min read
100 m² of roof under 50 mm of rain yields 4,500 litres. The area to enter is the footprint, not the sloping surface — and the 10 % missing is water the roof never delivers.
Marco Bianchi · 3 min read
At an 85 % learning rate, a task that takes 20 minutes first time reaches 8 minutes after 50 attempts. At 90 % it needs 415 — the same task, five points apart.
Aisha Karim · 3 min read
A straight run of copper going from 20 to 70 degrees gains 8.5 mm over ten metres. Steel gains 6 mm, and a 100-metre steel span over a 60-degree year moves 72 mm.
Marco Bianchi · 3 min read
A coefficient of 0.3 against a normal force of 100 N gives 30 N of friction, and the area never enters the formula. What does enter it, and is usually got wrong, is the normal force.
Marco Bianchi · 3 min read
A 20-metre fall takes 2.02 seconds and lands at 19.81 m/s. From 40 metres it takes 2.86 seconds and lands at 28.01 m/s — the speed is up by a factor of √2, and the energy by exactly two.
Lena Hoffmann · 4 min read