18 articles
Finance
- How to make a monthly budget with irregular expenses
- Compound interest with monthly contributions: formula and example
Knowledge Base
Practical explanations, worked examples and calculators for everyday decisions.
Browse categories
23 articles
Automotive
Explore articles6 articles
Metals
Explore articles10 articles
Date & time
- How to count business days: weekends, holidays and start dates
- Days between dates: inclusive counting, nights and working days
9 articles
Shopping
- Unit price explained: compare packs, bulk deals and discounts
- Reverse sales tax: find the price before tax
9 articles
Energy
Explore articles15 articles
Science
- Brine concentration by weight: a practical salt and water calculation
- Coefficient of variation: compare spread across different averages
5 articles
Business
- Website conversion rate: choose the right denominator
- ROAS versus profit: what a 4× return really means
Featured articles
How to make a monthly budget with irregular expenses
Build a realistic budget by converting annual bills into monthly amounts, checking cash flow and avoiding double-counted savings.
Compound interest with monthly contributions: formula and example
Separate deposits from growth and understand how contribution timing, compounding and inflation change a savings projection.
How to count business days: weekends, holidays and start dates
Avoid off-by-one deadline errors by defining the workweek, start-day rule and holiday calendar before counting.
How to make a monthly budget with irregular expenses
Build a realistic budget by converting annual bills into monthly amounts, checking cash flow and avoiding double-counted savings.
Compound interest with monthly contributions: formula and example
Separate deposits from growth and understand how contribution timing, compounding and inflation change a savings projection.
CAGR versus average growth
Use compound annual growth for endpoints and arithmetic average growth for period-by-period changes.
Percentage change vs percentage points: calculate the right difference
Compare price changes, rates and growth correctly, with worked examples, reverse calculations and common percentage mistakes.
Loan payments explained: monthly interest, principal and total cost
Check a fixed-rate loan payment, understand an amortization schedule and compare loan terms without focusing only on the monthly amount.
CAGR vs average annual return: formula and examples
Learn how to calculate compound annual growth rate, why it differs from an arithmetic average, and when neither number captures investment risk.
Mortgage down payment: monthly payment and total cost
Estimate how a larger down payment changes the loan principal, monthly payment and cash left after closing, with a worked example.
Emergency fund calculator: months of essential expenses
Build an emergency fund target from necessary monthly spending, choose a realistic saving schedule and avoid double-counting irregular bills.
Break-even point: units, revenue and margin explained
Find the sales volume needed to cover fixed and variable costs, with a worked example and practical limits for pricing decisions.
Inflation and purchasing power: what is a real return?
Use the inflation adjustment formula to compare future money with today’s purchasing power and distinguish nominal from real investment returns.
Debt snowball vs avalanche: which payoff order fits?
Compare the smallest-balance and highest-interest-rate methods, plan an extra payment and understand how fees and minimums affect the timeline.
Extra loan payments: interest saved and payoff date
See how an extra payment applied to principal can shorten a fixed-rate loan, and check prepayment rules before comparing scenarios.
50/30/20 budget rule: how to adapt it to your income
Split take-home income into needs, wants and savings, then adjust the percentages for your fixed costs and real goals.
Debt-to-income ratio: calculate it before a mortgage
Calculate monthly debt payments as a share of gross income and see why a lender’s affordability test involves more than one ratio.
APR vs interest rate: compare the real cost of a loan
Understand what the stated rate covers, how fees affect APR, and which loan details to compare before borrowing.
How much should I save each month to reach a goal?
Turn a target and deadline into a monthly savings amount with and without an assumed return.
Credit card interest: monthly estimate and daily balance
Understand the simple APR estimate before comparing it with a statement’s daily-balance calculation.
CAGR for a decline and the recovery needed afterward
Keep annualized change separate from the percentage needed to recover a loss.
How to calculate EV charging cost
Separate battery energy, charging losses and tariff fees before comparing home and public charging.
WLTP, CLTC, WLTC, EPA and NEDC range figures
Understand why driving-cycle range ratings are not interchangeable distance units.
PSI and bar for tire pressure
Convert pressure units while keeping gauge pressure and vehicle recommendations separate.
MPG, km/L and L/100 km explained
Understand reciprocal fuel economy and the difference between US and Imperial gallons.
Annual car ownership cost explained
Separate running costs, depreciation and finance without double-counting loan principal.
L/100 km to MPG: compare fuel economy and annual running cost
Convert US and imperial MPG correctly, estimate fuel bills and combine real driving records without averaging ratios incorrectly.
EV charging time: kWh, kW and charging losses
Estimate how long an electric vehicle takes to charge from one battery percentage to another, with a worked home-charging example.
EV vs petrol cost per trip: compare the same distance
Compare electricity and fuel for a journey using consumption per 100 km, energy prices and charging fees without confusing operating cost with total ownership.
Tire pressure in PSI, bar and kPa: check it cold
Convert tire pressure units correctly and find the recommended cold setting on the vehicle label instead of relying on the tire sidewall.
Car depreciation per mile: estimate the hidden driving cost
Combine purchase price, resale estimate and mileage to see the ownership cost that fuel-only comparisons miss.
EV home charging cost per year: a practical estimate
Use annual distance, energy per 100 km, charging losses and your electricity tariff to budget home charging.
How many EV charging stops do you need on a road trip?
Estimate charge stops from usable battery energy, real consumption and a comfortable arrival reserve before planning a long drive.
How a different tire size changes speedometer and distance readings
Compare tire diameters before changing wheel or tire size, and understand the speedometer estimate without confusing it with an approval.
How to estimate annual car mileage from daily driving
Turn commuting, weekend trips and occasional journeys into a realistic yearly distance and running-cost scenario.
Annual mileage for a lease or insurance quote: use odometer evidence
Project yearly driving from two odometer readings and check your allowance against a realistic buffer.
WLTP, EPA and CLTC EV range: why the numbers differ
Compare electric vehicle test-cycle labels without treating them as fixed real-world conversion factors.
EV charging cost with losses: home versus public charging
Separate battery energy from energy billed at the socket, then compare home and public tariff structures.
Tire size and rolling radius: calculate a speedometer change
Decode a size such as 225/55 R17 and compare diameter, circumference and indicated speed.
Tire circumference and revolutions per kilometre from a size marking
Turn nominal diameter into circumference and estimated revolutions, keeping millimetres, metres and kilometres consistent.
Annual mileage from two odometer readings
Estimate annual driving from actual readings, then compare the result with a weekly travel plan.
Power-to-weight in kW per tonne: compare like with like
Normalize power and vehicle mass before comparing a ratio.
Average trip speed: add the times of both legs
Use total distance and elapsed time when two parts of a journey have different speeds.
Round-trip fuel cost: count both directions once
Build a complete trip distance before multiplying consumption by the fuel price.
How to count business days: weekends, holidays and start dates
Avoid off-by-one deadline errors by defining the workweek, start-day rule and holiday calendar before counting.
Days between dates: inclusive counting, nights and working days
Choose the right date-counting rule for stays, schedules and planning, with examples that explain the common one-day difference.
Leap-day birthdays: age and date calculations
Calculate elapsed time for someone born on February 29 and understand why non-leap-year birthday conventions differ.
One month from today is not always 30 days
Learn why calendar-month addition differs from a fixed day count near February and month ends.
Schedule a meeting across time zones without a date mistake
Convert a meeting hour with the correct date, check daylight saving and send an unambiguous invitation.
Calculate work shift hours with breaks and overnight time
Find payable hours when a shift crosses midnight, and separate unpaid breaks from the time on site.
Countdown between dates: when to include the start and end day
Avoid an off-by-one error when counting a deadline, hotel nights, delivery window or event countdown.
Seven business days from Friday: count with holidays and cutoffs
Work through a Friday start date while distinguishing inclusive counting, weekends and local holidays.
Business days: inclusive counts versus adding a deadline
Separate counting a date interval from moving forward a number of working days.
Adding a calendar month is not adding 30 days
Understand month-end clamping and keep calendar arithmetic separate from business-day rules.
Unit price explained: compare packs, bulk deals and discounts
Find the better-value pack using one measurement basis, then account for discounts, delivery and waste.
Reverse sales tax: find the price before tax
Work backward from a tax-inclusive total using the correct formula, and distinguish removing tax from applying a discount.
Bulk discount or smaller pack: compare unit prices
Calculate the price per kilogram or item after coupons and multibuy offers, then decide whether a large package really saves money.
Stacked discounts and sales tax: find the final price
Calculate sequential promotions correctly and see why two discounts are not usually added together.
Price per serving versus price per 100 g: compare food packages
Compare package sizes fairly after accounting for edible yield, serving size and the unit printed on the shelf.
Percentage discount or fixed coupon: which deal is cheaper after shipping?
Compare offers by the final amount paid, including coupon rules, delivery charges and the tax treatment of discounts.
Dilute a brine by weight: use the total solution mass
Calculate added water from an existing salt solution and a lower target mass percentage without confusing water-only and solution-based ratios.
Fluid ounces and ounces: choose volume or mass before converting
Use the correct converter for fl oz and oz, and include density when changing between volume and mass.
Scale a bread recipe without changing hydration
Scale flour and water together, check baker’s percentages, and keep ingredient weights separate from volume measures.
Watts to kWh: calculate appliance electricity cost
Convert power and running time into energy, then estimate cost using actual tariffs and realistic operating hours.
Standby power cost: watts to annual kWh
Estimate the yearly electricity cost of an always-on device, and learn when a nameplate wattage is the wrong input.
Solar panel payback: calculate from your electricity bill
Estimate simple payback using installed cost, usable production, self-consumption and the tariff actually avoided.
Appliance duty cycle: estimate electricity cost when a device cycles on and off
Calculate energy use from watts, runtime and the fraction of time a compressor, heater or motor actually draws full power.
kW versus kWh: calculate energy from appliance power and time
Understand why a kilowatt measures instantaneous power and a kilowatt-hour measures consumed energy on a bill.
Battery backup runtime: estimate hours from Wh and device watts
Estimate how long a power bank or backup battery can run a device after usable capacity and conversion losses.
Series and parallel resistors: total resistance and current
Calculate equivalent resistance for simple circuits and check power before choosing parts.
Heat conduction: how thickness and area change the rate
Estimate steady heat flow through a flat layer while distinguishing watts, energy and material conductivity.
Carnot efficiency: use absolute temperatures, not Celsius ratios
Calculate an ideal heat-engine limit and compare it with efficiency from measured heat and work.
Brine concentration by weight: a practical salt and water calculation
Calculate salt percentage by total solution mass, with a clear example for a 3% brine and notes on displacement and food safety.
Coefficient of variation: compare spread across different averages
Learn when standard deviation divided by the mean is meaningful, with a comparison of two sample groups.
Arithmetic sequence: nth term versus sum of the first n terms
Distinguish a single term from a running total, with a step-by-step 5, 8, 11 sequence example.
How many hours should I study each day before an exam?
Turn your remaining topics, available days and realistic study blocks into a plan that you can follow.
Kinetic energy and speed: why doubling speed quadruples energy
Use mass and speed in compatible units, then compare scenarios without confusing energy with stopping distance.
How to add and subtract mixed fractions, step by step
Use improper fractions and a common denominator, then reduce and check the answer.
Cylinder volume from diameter and height: litres and cubic units
Convert diameter to radius first, use consistent units and distinguish internal capacity from external size.
When a coefficient of variation is misleading: a mean near zero
Check the denominator and measurement scale before interpreting standard deviation as a percentage of the mean.
Parallel resistors: why unequal branches draw different currents
Calculate each branch current at a shared voltage and check the total against equivalent resistance.
Vector projection: check the perpendicular remainder
Separate a vector into parallel and perpendicular parts, then verify the result with a dot product.
Voltage dividers: why a connected load changes the output
Compare an unloaded resistor divider with a loaded output using equivalent resistance.
Decibel changes: convert a difference into a power ratio
Interpret a logarithmic change without confusing power ratios, amplitude ratios and absolute sound levels.
Cone volume: radius, diameter and slant height
Choose perpendicular height for volume and reserve slant height for the side surface.
Weighted averages when group sizes are different
Combine group averages using the number of observations instead of giving every group equal influence.
Celsius and Fahrenheit: a change is not a reading
Convert temperature readings with the offset, but convert a temperature difference using only the scale factor.
Website conversion rate: choose the right denominator
Calculate conversion rate from visits and completed actions without mixing users, sessions or ad impressions.
ROAS versus profit: what a 4× return really means
Compare ad-attributed revenue with ad spend and include product costs before judging campaign profitability.
Conversion rate: sessions, users and repeat orders
Define both numerator and denominator before comparing a conversion percentage.
Break-even ROAS from contribution margin
Compare advertising revenue with the margin left to cover advertising cost.
CPM, impressions and reach: estimate an advertising budget
Keep displayed impressions separate from the people who may have seen them.