Mental math, tested live
Number Tricks & Mental Math
Short shortcuts that make everyday numbers easy. Type your own numbers into any trick to see the mental steps worked out.
01 · Percentages
The Percentage Flip
18% of 50 sounds hard. 50% of 18 is just 9 — and it's the same answer.
Why it works: “x% of y” means x × y ÷ 100. Multiplication doesn't care about order, so x% of y always equals y% of x.
Open the Percentage CalculatorTry it yourself
- 18% of 50 is the same as 50% of 18 — both equal 18 × 50 ÷ 100.
- Pick whichever order is easier to do in your head.
- 18 × 50 = 900, then ÷ 100 = 9.
= 9
02 · Multiplication
Multiply by 11 in 2 Seconds
Split the digits, add them, and drop the sum in the middle: 35 × 11 = 385.
Why it works: 11 × n = 10n + n. Writing it out, the tens and ones digits shift and overlap, so the middle digit is their sum.
Try it yourself
- Split 35 into 3 _ 5.
- Add the digits: 3 + 5 = 8.
- Put 8 in the middle: 385.
= 385
03 · Squares
Squaring Numbers Ending in 5
65² = 6 × 7 with 25 on the end = 4,225.
Why it works: (10a + 5)² = 100a² + 100a + 25 = 100 × a(a + 1) + 25. So the front is a × (a + 1) and the last two digits are always 25.
Try it yourself
- Drop the 5: the front part is 6.
- Multiply it by the next number: 6 × 7 = 42.
- Append 25: 4225.
= 4,225
04 · Growth
The Rule of 72 & Rule of 115
Divide 72 by a yearly rate to estimate doubling time; divide 115 to estimate tripling.
Why it works: Doubling time is ln(2) ÷ ln(1 + r). For everyday rates that works out close to 72 ÷ rate; ln(3) gives roughly 115 ÷ rate for tripling.
Open the Interest CalculatorTry it yourself
- Doubling: 72 ÷ 8 ≈ 9 years (exact with yearly compounding: 9).
- Tripling: 115 ÷ 8 ≈ 14.4 years (exact: 14.3).
- The shortcuts are most accurate for rates around 6–10%.
= 9 yrs to double · 14.4 yrs to triple