Science & education writer at OneKitly
Math, physics and statistics explainers
Lena makes math, physics and statistics click. She writes clear explainers that connect textbook formulas to the problems people actually need to solve.
Lena states the formula, where it comes from and where it stops working. Each explainer carries a worked example a reader can check by hand, and every approximation says what it costs — the assumption it makes and the range over which it holds.
Ranked by how many pages of this site link to them, not by traffic.
Guides published under this byline in each section. Each link opens the section in full, across all writers.
· 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.
· 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.
· 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.
· 6 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.
· 4 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.
· 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.
· 4 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.
· 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.
· 3 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.
· 4 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.
· 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.
· 3 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.
· 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.
· 3 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.
· 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.
· 7 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.
· 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.
· 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.
· 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.
· 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.
· 4 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.
· 3 min read
For 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.
· 3 min read
Five points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.
· 3 min read
A mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.