Guides behind the calculators.
Every guide here explains a formula one of our calculators implements — with the arithmetic worked in full, so you can check every number by hand.
Scheduling Across Time Zones: Why Your Meeting Moved an Hour
Why standing meetings between the US and Europe slide an hour every March, and the date-aware conversion habit that keeps cross-zone invites honest
2026 Retirement Contribution Limits: 401(k), IRA and Catch-Ups
Every 2026 retirement limit from IRS Notice 2025-67 — 401(k), IRA, both catch-ups and the Roth phase-outs — with the arithmetic behind each ceiling shown
Quarter-Mile Times: What Horsepower-to-Weight Really Buys
How the Fox, Huntington and Hale cube-root formulas turn weight and horsepower into a quarter-mile ET — and where those empirical fits stop holding
Dog Years: Why 'Multiply by Seven' Is Wrong
A one-year-old dog is about 15 human years old, not 7 — how the AAHA breed-size chart and a 2020 DNA-methylation formula really convert dog years
Counting Days Between Dates: Inclusive, Exclusive and Business Days
Monday to Friday is four days or five depending on the convention. The +1 rule for inclusive counting, clear days, and business-day counts worked in full.
TDEE and Energy Balance: The Arithmetic of Maintenance Calories
How a TDEE estimate is actually built — Mifflin-St Jeor BMR, activity multipliers, the thermic effect of food — and how wide its error bars really are
Race Pace: Predicting Your Marathon From a 10K
How the Riegel 1.06 exponent turns a 10K result into a marathon prediction, worked digit by digit — plus the limits every race time predictor inherits
MPG vs L/100km: Two Ways to Measure the Same Tank
Convert MPG to L/100km with one constant — 235.215 — and see why the same 5 MPG gain saves about nine times more fuel at the low end of the scale
Standard Deviation: What It Measures and When the Mean Misleads
Two datasets with the same mean can behave nothing alike — how standard deviation is built step by step, and when to divide by n versus n−1
The 'At Least One' Trick: Complement Probability
Why 1 − P(none) answers every "at least one" question — worked through dice bets, card draws and the birthday problem, plus the adding mistake that breaks it
BMI's Limits: What the Index Measures and What It Can't
BMI is exact arithmetic and a solid population screen, but a poor individual body-fat measure — where the index works, where it fails, and what children use instead
USDA Food Yields: Why Recipes Measure Before and After Cooking
What USDA food yields measure, why cooked and raw weight are different numbers, and the double-counting mistake that oversizes every holiday turkey
Turkey Cooking Times: The Heat-Transfer Math Behind the Chart
How long to cook a turkey at 325°F, why minutes-per-pound falls from 20.6 to 12.5 as birds get bigger, and the USDA chart read as one continuous curve
Percent Off, Percent Change and the Discount Stack Trap
Why 20% off then 10% off is 28% off, not 30 — the one-line percent-off formula, a 10% mental-math anchor, and how stacked discounts and sales tax compound
Roman Numerals: The Rules, the Exceptions, and Why MCMXCIX Isn't MIM
The seven symbols, the six legal subtractive pairs, why 1999 is MCMXCIX rather than MIM, and the clock-face IIII that breaks the rules on purpose
Cups, Grams and Why Serious Bakers Weigh Everything
100 mL of milk is about 0.42 US cups. A cup of flour is 120 g or 150 g depending on how you fill it — density is why volume lies, and why bakers weigh
Binary and Hex: Number Bases Programmers Actually Use
How place value turns binary 10110100 into 180 and 0xB4, plus a complete hex-to-binary chart and the grouping mistake that silently doubles a conversion
M-Pesa Charges in 2026: How the Tariff Bands Work
Safaricom's full 2026 send and withdrawal tariff tables, why one extra shilling can raise the fee 77%, and the band-boundary maths that decides what you pay
KRA PAYE: How Kenya's Income Tax Bands Actually Apply
Kenya's 2026 PAYE bands, the statutory deductions that shrink taxable pay first, and a full walkthrough of what a KES 80,000 salary actually pays
NSSF, SHIF and Housing Levy: Kenya's Payroll Deductions Explained
Kenya's statutory payroll stack — NSSF Year 4 tiers, SHIF at 2.75%, the 1.5% housing levy and PAYE — explained and walked through one payslip to net pay
Net Worth: What Counts, What Doesn't, and Why Yours Swings
Which assets and debts actually count in a net worth calculation, the valuation rule for each line item, and why the total swings in quarters when your habits don't
Loan-to-Value: The Ratio That Decides Your Mortgage Terms
What a 100% loan-to-value mortgage means, why the 80% LTV line triggers PMI, and how the ratio gets re-measured when you refinance — with worked examples
CD Ladders: Locking Rates Without Locking All Your Cash
How a five-rung CD ladder works, with every maturity value computed step by step — plus what breaking a CD really costs and when a T-bill beats the shortest rung
Pixels to Print Size: What DPI Actually Does
An 11×14 print needs 3300 × 4200 pixels at 300 PPI. The full 300 DPI size chart, where that number comes from, and when far less resolution looks identical
Debt Avalanche vs Snowball: The Math and the Psychology
Same three debts, same $605 budget, two orderings — what the avalanche saves in interest, what the snowball buys in momentum, and when each wins
Compound Interest: Why Starting Early Beats Finding a Better Rate
What compound interest is, the formula behind it, and honest arithmetic showing why ten extra years of compounding beats two extra points of return
GRE Scores and Percentiles: Reading Your Report
How ETS percentile ranks work on the 2026–27 GRE tables, why a 160 Verbal and a 160 Quant land 32 percentile points apart, and what counts as a good score
dBm to Watts: RF Power Levels Without a Lookup Table
What 1 dBm is in watts, the formula behind the dBm scale, and the mental rules — 10 dB is a decade, 3 dB a doubling — that replace the lookup table
Battery Capacity: Why mAh and Wh Tell Different Stories
Why a 20,000 mAh power bank holds one sixth the energy of a 12,000 mAh e-bike pack — how voltage turns charge into watt-hours, with worked examples.
Test Grades: Converting Wrong Answers Into Percentages and Letters
What 11 wrong out of 50 works out to (78%, a C), a full wrong-answer chart for 50-question tests, and why the same mistakes grade differently on shorter ones
Kinematic Viscosity of Air: Why Every Aerodynamics Problem Starts Here
Why air's kinematic viscosity is 1.51×10⁻⁵ m²/s at 20 °C: the Sutherland's law arithmetic, the pressure dependence tables hide, and the Reynolds numbers it feeds
Weighted vs Unweighted GPA: Which Number Colleges Actually Read
How weighted and unweighted GPAs differ, the AP/IB bonus-point conventions, and why admissions offices recalculate your number before comparing applicants
Parallax: How We Measure the Distance to Stars
The parallax distance formula d = 1/p explained — why the parsec makes it exact, worked examples from real catalogues, and the 20% rule for Gaia-era parallaxes
Linear Feedback Shift Registers: Pseudo-Randomness From Four Flip-Flops
What an LFSR is, how tap choice sets its period, and a 4-bit register traced through every state of its maximal-length cycle — taps, seeds and the zero trap
Harmonic Numbers: The Series That Grows Forever, Slowly
The harmonic number formula — exact sum and the ln n + γ estimate — worked in full for H₁₀, plus why the harmonic series has no finite sum
Wire Gauge Explained: Why Thicker Wire Has a Smaller Number
What an AWG number actually measures, the three-steps-to-double geometry behind the scale, and why gauge alone never tells you how many amps a wire can carry
Scale Drawings: Reading 1:50 Plans Like a Builder
What 1:50 means in centimetres, how to convert drawing lengths in both directions, and the resizing, unit and area traps that misread floor plans
Reading Military Time: The 24-Hour Clock Without Mental Math
The full 12-hour to 24-hour conversion chart, the one add-12 rule behind it, why noon is 1200 but midnight is 0000, and what a four-digit time never tells you
Vitamin D Units: Micrograms vs IU, and Why Labels Mix Them
Why 1 microgram of vitamin D equals exactly 40 IU, how to read labels that print both units, and the unit mix-ups that produce thousand-fold errors
The Ankle-Brachial Index: Why the Higher Arm Wins
How the ankle-brachial index is calculated, why the denominator takes the higher of the two arm pressures, and how far the ratio drifts when it doesn't
ANC: How the Absolute Neutrophil Count Is Calculated
The ANC formula — WBC × (segs% + bands%) ÷ 100 — worked digit by digit, the unit notations labs use, and the arithmetic slips that corrupt the count
Subnetting and CIDR Notation, Explained From Zero
What the number after the slash in 192.168.10.0/26 counts, how it maps to a subnet mask, and worked /24 and /26 address ranges — from first principles
MOSFET Threshold Voltage: What V-th Actually Marks
What a MOSFET's threshold voltage marks, the test-current convention datasheets use to measure it, and how body bias and temperature move the real number
What College Acceptance Rates Actually Tell You
How acceptance rates are calculated, why the published percentage is not your personal odds, and how yield and application volume move the number
Watts, Amps and Volts: The Household Electricity Triangle
How volts, amps and watts relate, how to convert watts to amps at any voltage, and why breakers trip on current while your bill only counts power
How Long Do Stars Live? The Mass-Lifetime Relation
Why mass alone decides a star's lifespan — the stellar lifetime formula worked in full for the Sun, a ten-solar-mass star and the red dwarfs that never die
The Real Cost of Paying the Credit Card Minimum
A $5,000 balance at 20.99% APR takes 672 months — 56 years — to clear at a 2% minimum. The full amortization, worked honestly, and what a fixed payment saves
What Does FPPG Mean in Fantasy Football?
FPPG — fantasy points per game — is the number on every DraftKings and FanDuel player card. What it measures, how scoring changes it, and the traps that make it lie.
Golf Score Differentials and Handicaps, Explained
How the World Handicap System turns a round of golf into a Score Differential, how eight of your last twenty become a Handicap Index, and the arithmetic at every step.
Cricket Statistics Explained: Batting Average, Strike Rate, Economy and Required Run Rate
What every number on a cricket scorecard measures, how each is calculated — with worked examples — and the overs notation mistake that corrupts run rates.