Blog
Occasional Random thoughts from us.
How to Calculate Standard Deviation
Standard deviation measures how spread out data is around its average. Here is the step-by-step calculation with a worked example, the difference between population and sample formulas, and the 68–95–99.7 rule.
How to Find Prime Factors
Every whole number above 1 breaks down into primes in exactly one way. Here are three methods to find prime factors, from factor trees to Fermat's 1643 trick, plus how to use a factorization to count divisors instantly.
How to Find the Least Common Multiple
The least common multiple tells you when repeating cycles line up, from bus schedules to cicadas that emerge together once every 221 years. Here are three methods to find the LCM, with worked examples.
How to Find the Greatest Common Factor
The greatest common factor is the largest number that divides two or more numbers evenly. Here are three methods, from listing factors to Euclid's 2,300-year-old algorithm, with examples and everyday uses.
How to Calculate Percent Change
Going from 50 to 80 is a 60% increase, but going back from 80 to 50 is only a 37.5% decrease. Here is the percent change formula, why the direction matters, and when to use percentage points or log changes instead.
How to Calculate the Area of a Circle
One 18-inch pizza has more pizza than two 12-inch pizzas. Here is how to calculate a circle's area from its radius, diameter or circumference, with worked examples and the 3,600-year-old Egyptian shortcut.
How to Calculate a Square Root
You can find √1500 to six decimal places by hand in three steps. Here are four methods for calculating square roots, from recognizing perfect squares to simplifying radicals and the ancient Babylonian method.
How to Calculate an Average
Drive 60 mph one way and 40 mph back, and your average speed isn't 50 mph. Here is how to calculate the mean, median and mode, plus the geometric and harmonic means for growth rates and speeds.
How to Calculate a Percentage
Every percentage question is one of three types: find the part, find the percent, or find the whole. Here is one formula that handles all three, with worked examples, mental math shortcuts and common mistakes.