Coin Flip Probability: Streaks, Odds, and the Gambler's Fallacy
Coin flip probability for sequences, at least one head, and k heads in n flips, plus why streaks happen and how to get a fair result from a biased coin.
Tooljip Blog
Practical, plain-English guides to PDFs, images, text and data formats, everyday math, and time management. Each article answers one question clearly.
How to Compress Images for Web Without Visible Quality Loss
Learn the right order to compress images for the web: resize for real display size, pick a format, tune quality, strip metadata, and check results by eye.
How Random Number Generators Work: Pseudo-Random vs. True Random
Learn how random number generators work, from seeds and LCGs to secure and hardware randomness, and how to pick numbers in a range without modulo bias.
How to Calculate Percentages: 5 Formulas for Everyday Math
Calculate a percentage of a number, percent change, and original prices before discounts or tax, with worked examples and mental-math shortcuts.
JPG vs PNG vs WebP: Which Image Format Should You Use?
Compare JPG, PNG, and WebP: lossy vs. lossless compression, transparency, animation, and support, plus a use-case table and tips for safe conversion.
How to Merge PDF Files: Page Order, Bookmarks, and Pitfalls
Learn how to merge PDF files with desktop apps, browser tools, or qpdf, plan page order, and avoid problems with bookmarks, forms, and signatures.
Percentage Points vs Percent: What's the Difference?
Learn the difference between percentage points and percent change, with examples, basis points, compounding, and why a 50% loss needs a 100% gain.
The Pomodoro Technique: How It Works and How to Adapt It
Learn the Pomodoro Technique: the 25/5 cycle, why short timed blocks help, how to handle interruptions, and variants like 50/10, plus a sample day.
How to Reduce PDF File Size Without Ruining Quality
Learn what makes PDFs large and how to reduce PDF file size with image downsampling, JPEG recompression, and cleanup, without blurry text or broken links.
To-Do List Methods Compared: Eisenhower, 1-3-5, Ivy Lee, GTD
See one task list organized four ways (Eisenhower Matrix, 1-3-5, Ivy Lee, and GTD), then pick the right method and fix the reasons to-do lists fail.
What Is a Unix Timestamp? Converting Epoch Time to Dates
Learn what a Unix timestamp is, how to tell seconds from milliseconds, convert epoch time to dates by hand or in code, and why 2038 matters.
What Is Base64? How Base64 Encoding Works and When to Use It
Learn what Base64 is, how it turns bytes into text step by step, why output grows by about 33%, what = padding means, and when to use it.