· 3 min read
How to Calculate a Weighted Average
A weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.
Articles by Lena Hoffmann
Science & education writer · View profile
· 3 min read
What Week Number Is It?
Week numbers run from 1 to 52 or 53. Here's how the ISO 8601 system numbers them, why some years have 53 weeks, and where businesses use them.
· 3 min read
Combinations vs Permutations: When Order Matters
The difference between combinations and permutations comes down to one question: does order matter? Learn the nCr and nPr formulas with clear worked examples.
· 3 min read
How to Add or Subtract Days from a Date
Count forward to add, backward to subtract, rolling over month ends. Here's how, why month lengths and leap years trip you up, and when weekends count.
· 3 min read
Seconds, Minutes and Hours: How Time Units Fit Together
The relationships behind 60 seconds, 60 minutes, 24 hours and 86,400 seconds a day, with quick conversions you can reuse.
· 4 min read
How Many Days Until My Birthday? (Step by Step)
Find the exact days to your next birthday, including the tricky case where this year's date has already passed.
· 3 min read
How Exponents Work: Powers and the Laws of Exponents
An exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.
· 3 min read
How to Calculate Percent Error: The Accuracy Formula for Science
Percent error tells you how close a measurement is to the true value. Learn the formula, work through an example, and see how scientists use it to judge accuracy.
· 4 min read
How to Find the Area of a Triangle: Base × Height and Heron's Formula
Two reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.
· 3 min read
What Is a Leap Year? The /4, /100, /400 Rule Explained
Why some years have a February 29, how the divisible-by-4, -100 and -400 rules combine, and how to check any year quickly.
· 4 min read
How Many Days Until a Date? (With Worked Examples)
Count the days until any future date, understand inclusive vs. exclusive counting, and build an accurate countdown you can trust.
· 3 min read
Percentage Difference vs. Percentage Change vs. Percentage Error
Three percentages that look alike but answer different questions. Learn the formula for each, when to use it, and why they give different numbers.
· 14 min read
Tournament Brackets: Byes, Seeds, and Why the Numbers Must Be Powers of Two
A knockout bracket halves its field every round, so it only closes on a power of two. The bye count, the round count, the seed order and the total number of matches all follow from that one fact — and each is a one-line derivation.
· 14 min read
Splitting People Into Fair Groups: Random and Fair Are Not the Same Requirement
23 people do not divide into fours, and a uniformly random split can hand one group every strong player. Here is the remainder arithmetic, the measured cost of pure randomness, and the stratified fix.
· 13 min read
Poker Hand Probabilities, Derived Rather Than Memorised
Every five-card poker probability is a counting argument over 2,598,960 hands, and each one fits on a single line. Here are all nine, with the check that proves them: the counts must sum to exactly C(52,5).
· 13 min read
Shuffling Is Harder Than It Looks: A Million Runs of the One-Line Shuffle
The shuffle everyone writes — sorting with a random comparator — is biased, and not slightly. A million measured runs show eight of the twenty-four orderings turning up twice as often as the other sixteen.
· 13 min read
Stacked Discounts Do Not Add Up
Twenty percent off and then a further ten percent off is not thirty percent off — it is twenty-eight, because the second discount applies to the already-reduced price. The general rule, the cases where order matters, and how sales tax changes the answer.
· 14 min read
Percentage Points Are Not Percent
Moving from 4% to 5% is a rise of one percentage point and a rise of twenty-five percent. Both statements are true, which is exactly why the ambiguity is so easy to exploit — and why basis points exist.
· 15 min read
Date Arithmetic Is Harder Than It Looks
"One month later" has no single correct answer, and every date library has had to pick one. Month addition is neither associative nor invertible, a day is not always 24 hours, and age is not days divided by 365.25.
· 15 min read
Leap Years: The Rule, the Exception, and the Exception to the Exception
Divisible by four, except centuries, except centuries divisible by four hundred. The three-line rule exists because the tropical year is not 365.25 days, and the arithmetic behind it explains ten deleted days in 1582 and a calendar that repeats exactly every 400 years.