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