Calculators that show their working
144 of them, across building materials, money, health, business and everyday maths. Put in your numbers, get the answer — and the formula it came from.
No calculator matches that.
Matching calculators
- 15 vs 30 year What the shorter term costs each month, and what it saves over the loan.
- Retirement account What a workplace account grows to, with the employer match counted properly.
- Age Exact age in years, months and days, and when the next birthday falls.
- Amortization schedule Where each payment goes, year by year, and how slowly the balance actually falls.
- Angles Degrees, radians, gradians and turns.
- Area Area of a rectangle, circle or triangle, in several units, with the formula.
- Asphalt Tonnage for a driveway or car park, by area and compacted depth.
- Average Paste a list of numbers and get every kind of average at once.
- BMI Body mass index, the band it falls in, and the healthy weight range for your height.
- BMR What your body spends doing nothing, and what activity adds to it.
- Air conditioner size What size of unit a room needs, with ceiling height, sun and occupancy allowed for.
- Baseboard & trim How many lengths of skirting, coving or picture rail a room takes.
- Biweekly payments What paying half the mortgage every fortnight actually saves, and why.
- Board foot Board feet and the cost of them, worked out on the nominal size the yard bills.
- Body fat Body fat from a tape measure, using the US Navy method.
- Break-even How many units cover the fixed costs before anything is profit.
- Brick How many bricks a wall takes, worked out from the brick size and the mortar joint.
- CAGR The annual rate that turns a starting value into an ending one.
- Calorie deficit What to eat, how fast the weight comes off, and how long it takes.
- Calories burned What an activity costs, and how much of that you would have burned anyway.
- Car affordability What a monthly budget buys once insurance, fuel and upkeep come out of it.
- Car loan Monthly payment and total interest on car finance, at your own rate.
- Circle Radius, diameter, circumference and area — give any one, get the rest.
- Closing costs What you actually need on the day, beyond the deposit.
- Commission What a rate actually pays once the threshold is taken into account.
- Compound interest What a balance grows to, and how much of it is growth rather than deposits.
- Concrete bags How many bags of pre-mixed concrete a pour takes, in 40, 50, 60 or 80lb bags.
- Concrete block Block counts, courses and mortar for a CMU wall, with openings taken off.
- Concrete slab Work out how much concrete a slab needs, in cubic yards, cubic metres or bags.
- Cost per mile What running a vehicle actually costs per mile, once everything is counted.
- Countdown How long until a date, in days, weeks, months and working days.
- Credit card payoff How long a balance takes to clear, and what paying only the minimum costs instead.
- Add to a date What date falls a given number of days, weeks or months away.
- Days between dates Days, weeks, months and working days between any two dates.
- Debt consolidation Whether one loan really costs less than the debts it replaces.
- Debt payoff plan Which debt to attack first, and what each order costs you.
- Decimal to fraction Any terminating decimal as a fraction in lowest terms.
- Decking Board rows, linear feet, joists and screws for a deck.
- Direct vs regular funds What the distributor commission inside a regular plan costs you over the years.
- Discount What you pay after one discount, or two stacked on each other.
- Divisibility Which numbers divide in exactly, and the rule that tells you without dividing.
- Journey time How long a drive really takes, once the average speed and the stops are honest.
- Drywall Sheets, screws, compound and tape for a room, with the openings taken off.
- Charging cost What charging an electric car costs, including the energy that never reaches the battery.
- Charging time How long a charge takes, given what the car will accept as well as what the charger offers.
- Electric vs petrol A year of driving, priced both ways, with charging losses counted.
- Employee cost What a hire actually costs, which is not the salary.
- Engine displacement Capacity from bore, stroke and cylinder count — plus what the bore-to-stroke ratio says about it.
- Exponents Any number to any power, with its squares, cubes and roots.
- Extra payment What paying a bit more each month saves in interest, and how many years it cuts.
- Financial independence How long until the portfolio covers the spending, at your saving rate.
- Fencing Posts, rails, pickets and concrete for a run of fence.
- Flooring Square footage for a room, plus how many boxes it takes with waste allowed for.
- Footings & columns Concrete for a strip footing or a set of round piers, by the yard and by the bag.
- Fractions Add, subtract, multiply or divide two fractions, simplified.
- Freelance rate What to charge to take home what you need, once unbillable time is paid for.
- Fuel cost What a journey costs in fuel, from the distance, the economy and the pump price.
- Fuel economy MPG to L/100km and back, with both gallons kept apart.
- Fuel savings What changing to a more efficient vehicle is worth over a year, and over five.
- Range on a tank How far a full tank goes, what it costs to fill, and the range worth planning to.
- GCF & LCM The greatest common factor and lowest common multiple of two numbers.
- Gravel How much gravel or crushed stone an area needs, by the ton and by the yard.
- Line of credit The interest-only payment, and what it becomes when the draw period ends.
- Heart rate zones Five training zones, by percentage of maximum or by heart-rate reserve.
- Home equity What share of the house is yours, and what a lender would advance against it.
- Horsepower Convert between hp, kW and PS, and work out the torque behind the power.
- Hourly to salary Annual, monthly and weekly pay from an hourly rate, allowing for unpaid weeks.
- Ideal weight Four published formulas, and how far apart they are.
- Insulation Batts or rolls for a wall or ceiling, with the framing taken out.
- Lean body mass Everything that is not fat, by three formulas or from a measured percentage.
- Lease vs buy Both payments side by side, with the car you own at the end counted properly.
- Length Millimetres, centimetres, metres, inches, feet and yards.
- Long division The quotient, the remainder, and every step of the working in between.
- MPG from a tank Work out what your vehicle actually returns, from a tank of fuel and the distance it covered.
- Macros A calorie target split into grams of protein, carbohydrate and fat.
- Markup What a markup actually leaves you, and why it is not the margin.
- Mileage claim What business miles come to at your rate, and how much of it the fuel actually was.
- Minimum payment What paying only the minimum costs, and what simply not lowering it saves.
- Affordability What a monthly payment you can manage translates into as a purchase price.
- Mortgage payment Monthly payment, total interest and what the first payment actually pays off.
- Discount points Whether buying down the rate pays back, and in what month.
- Mulch How much mulch a bed needs, in cubic yards or two cubic foot bags.
- Number in words Any number written out, in both the international and Indian systems.
- One-rep max Estimated 1RM from a set, by two formulas, with a training percentage table.
- Overtime pay Basic and overtime pay for a week, at any threshold and multiplier.
- Mortgage insurance What mortgage insurance costs, and when you can get rid of it.
- Leave accrual How much paid leave you have earned so far, and how much is left.
- Paint Work out how much paint a room needs, with the doors and windows taken off.
- Pay rise What a rise is worth in money, and what it is worth after inflation.
- Percentage What is X% of Y, X is what percent of Y, and the change between two numbers.
- Perimeter The distance round a rectangle, square, circle or triangle.
- Personal loan The payment, and the rate you are really paying once the fee comes out.
- Place value What each digit of a number is worth, and where it sits.
- Plywood & sheet goods How many sheets a floor, roof or wall takes, in any sheet size.
- Pool volume How many gallons a pool holds — rectangle, round, oval or kidney.
- Price per unit Which of two sizes is actually cheaper.
- Prime factors Break a number into the primes it is made of, in index form as well.
- Profit margin Margin, markup and profit from a cost and a price — and why the two percentages differ.
- Profit & loss Profit or loss from cost and selling price, as an amount and as a percentage.
- Protein intake How much protein a day, as a range rather than a number.
- Pythagoras Find the missing side of a right-angled triangle.
- ROI What came back against what went in, and what that is a year.
- Ratio Simplify a ratio, or scale one up to find the missing value.
- Refinance break-even How long the lower payment takes to pay back what the refinance costs.
- Roman numerals Numbers to Roman numerals and back, with the pieces it was built from.
- Roofing Roof area, squares and shingle bundles, with the pitch properly accounted for.
- Roth vs traditional Pay the tax now or later — and why the answer is just one comparison.
- Rounding Round to any place, and see which digit decided it.
- Running pace Pace per kilometre and per mile, with the race times it produces.
- Regular investing What investing a fixed amount every month grows to, with an annual step-up.
- Salary to hourly What a salary works out at per hour, once you count the hours honestly.
- Sales tax & VAT Add tax to a price, or pull it back out of one that already includes it.
- Sand How much sand a paver base, sandbox or bedding layer needs, by weight and volume.
- Savings goal What you need to put away each month to reach a target by a date.
- Simple interest Interest on the original sum only, with compound shown beside it for comparison.
- Slope Slope, distance and midpoint between two points.
- Sod & grass seed Rolls and pallets of turf for a lawn, or the seed to do it the slow way.
- Solar array size How large an array your electricity use needs, in kilowatts and in panels.
- Speed mph, km/h, metres per second, knots and feet per second.
- Stairs Risers, treads, total run and stringer length from your floor-to-floor height.
- Student loan The payment, and what the interest accruing before repayment adds to it.
- Student refinance What a lower rate saves, and what refinancing federal debt gives up.
- TDEE & calories Daily calories to maintain, lose or gain, with a macro split.
- Temperature Celsius, Fahrenheit and Kelvin — the one conversion that is not a factor.
- Tile How many tiles a floor or wall takes, with the grout gap and waste counted in.
- Time units Seconds, minutes, hours, days, weeks and years.
- Time duration Add up hours and minutes without a calculator getting it wrong.
- Times table The full table for any number, as far up as you need it.
- Timesheet Hours and pay for a week, from clock times, with breaks and overtime.
- Topsoil How much topsoil a bed or lawn needs, in cubic yards, bags and tons.
- Towing & payload Whether an outfit is inside both weight limits, not just the obvious one.
- Triangle Area and all three angles from three sides — no height needed.
- Trip cost Fuel, tolls and parking for a journey, split between everyone in the car.
- Tyre size What a tyre size actually measures, and what changing it does to the speedometer.
- Unit converter Length, weight, area and volume, converted with exact factors.
- Unitary method Find what one costs, then find what any number costs.
- VO2 max From a twelve-minute run, or from your resting and maximum heart rates.
- Volume Volume and surface area of a cube, box, cylinder, sphere, cone or pyramid.
- Waist to height The measure that beats BMI, and needs one number BMI ignores.
- Wallpaper Rolls needed, counted in drops, with the pattern repeat allowed for.
- Water heater size What size tank a household needs, sized on its busiest hour rather than its day.
- Water intake A starting figure from your weight and how much you train.
- Weight Kilograms, grams, pounds, tonnes and both kinds of ton.
- Working days Business days between two dates, weekends excluded.
Building & materials
Work out how much to order for a job — concrete, paint, flooring, roofing, decking, fencing and the rest.
- Concrete & aggregate
- Inside the house
- Decks, fences & roofs
- Garden & landscaping
- Brick & block
- Heating, water & power
Money & credit
Mortgages, loans, savings and paying down debt.
- Mortgages & home loans
- Loans & credit
- Paying off debt
- Saving & investing
- Investing & retirement
Health & fitness
Body measures, calories and training numbers.
- Body measurements
- Calories & nutrition
- Training & fitness
Business & work
Margins, break-even, pay and hours.
- Pricing & profit
- Pay & hours
Vehicles & fuel
Fuel costs, economy, charging, tyres and what a journey actually costs.
- Fuel & economy
- Electric vehicles
- Journeys & mileage
- Tyres & engines
Everyday maths
Percentages, fractions, areas, unit conversions and dates.
- School maths
- Numbers & arithmetic
- Shapes & geometry
- Unit conversion
- Dates & time
Most used
- Concrete slab Work out how much concrete a slab needs, in cubic yards, cubic metres or bags.
- Mortgage payment Monthly payment, total interest and what the first payment actually pays off.
- Paint Work out how much paint a room needs, with the doors and windows taken off.
- BMI Body mass index, the band it falls in, and the healthy weight range for your height.
- Percentage What is X% of Y, X is what percent of Y, and the change between two numbers.
- Roofing Roof area, squares and shingle bundles, with the pitch properly accounted for.
- Compound interest What a balance grows to, and how much of it is growth rather than deposits.
- Profit margin Margin, markup and profit from a cost and a price — and why the two percentages differ.
Numbers worth knowing
The figures that come up often enough to be worth carrying — for sanity-checking a quote, an order, a quoted rate or a claim someone has made.
Ordering materials
- A cubic yard of concrete
- covers 81 sq ft at 4 inches thick, or takes 45 80lb bags to mix by hand.
- A gallon of paint
- covers about 350 sq ft per coat. A 12×10 room has 352 sq ft of wall, not 120.
- A roofing square
- is 100 sq ft and takes 3 bundles of shingles.
- A 6/12 roof pitch
- makes the roof 12% larger than the ground beneath it. A 12/12 makes it 41% larger.
- A cubic yard of mulch
- covers 108 sq ft at 3 inches deep — about 14 two-cubic-foot bags.
- A cubic yard of gravel
- weighs roughly 1.4 tons. Topsoil is lighter, at about 1.13.
- 100 sq ft of 12-inch tile
- is 99 tiles once a 3mm grout gap is allowed for, not 100.
- 100 ft of fence at 8ft spacing
- needs 14 posts — 13 bays, plus one for the far end.
- A “2×6” deck board
- is really 5.5 inches wide, and a 4×4 post is 3.5 inches.
- Waste to allow
- 10% laying straight, 15% on a diagonal, 5–10% on concrete.
Borrowing and saving
- The first payment on a 30-year mortgage
- at 6.5% is 86% interest — $1,625 of a $1,896.20 payment, with only $271 coming off the debt.
- An extra $100 a month
- on that same loan saves $60,995 in interest and clears it 4 years early.
- Paying only the minimum
- on a $5,000 card at 22% takes over 60 years and costs $35,958 in interest.
- Money doubles
- in roughly 72 ÷ the rate years. At 7% that is about 10 years, and it is accurate to within a couple of months.
Body and training
- A pound of body fat
- is about 3,500 calories, so a 500 a day deficit is roughly a pound a week.
- The top of the healthy BMI range
- is 169 lb at 5ft 9in, and BMI counts muscle as weight, so it misreads the very lean.
- Zone 2 for a 40-year-old
- is roughly 108–126 bpm, from an estimated maximum of 180.
Pricing and pay
- A 50% markup
- is a 33% margin. They are not the same number and mixing them up is expensive.
- 30% off, then a further 20%
- is 44% off, not 50. Stacked discounts multiply rather than add.
- An employee
- costs 1.25 to 1.4× their salary once employer taxes, insurance and benefits are counted.
Running a vehicle
- Five more miles per gallon
- saves twelve times as much fuel at 10 mpg as it does at 40. MPG is a reciprocal, so equal steps are not equal savings.
- Fuel
- is only about a fifth of what a mile really costs. Depreciation is usually the largest line and nobody writes a cheque for it.
- 32 mpg in the US
- is 38.4 mpg in the UK. The car did not change — an imperial gallon is 20% larger.
Everyday sums
- 4,749 to the nearest hundred
- is 4,700. Only the tens digit decides it, and the 9 after it has no say.
- Adding 25% then taking 25% off
- leaves you at 375, not 400. The second percentage was of a bigger number.
- Two cars at 10 and 50 mpg
- average 16.7 mpg over the same distance, not 30. Reciprocals cannot be averaged.