Unit-Price Comparator
Price ÷ quantity across items — cheapest per unit highlighted.
Free tools
Each one runs the exact arithmetic its chapter teaches you to do by hand — and cites the chapter, so it backs up the book rather than replacing it.
Price ÷ quantity across items — cheapest per unit highlighted.
One discount or several stacked — why 20% then 10% is 28% off, not 30%.
“3 for $5” vs singles — the real price per item, and what you’ll use.
Price ÷ uses — when the dearer thing that lasts is the cheaper one.
Your own bands → tax, effective rate, marginal rate.
Subtract your own deductions (% or fixed) to find take-home.
Convert either way, and price up time-and-a-half.
Rebuild gross from hours & rate; compare with the payslip.
Units × rate + standing charge → bill total & cost per day.
Any billing cycle → real yearly total & monthly equivalent.
Two or three plans on the same usage — unit rate plus standing charge.
Meter readings vs the estimate — over- or under-charged, in money.
Annualise every subscription and total the yearly bite.
Cost per mile for petrol vs electric, and the yearly difference.
Lump sum + monthly saving compounded; growth vs what you put in.
Doubling time, rate needed, and projected growth.
What delaying the start really costs by the same end date.
The monthly amount to hit a target by a date, interest included.
Turn a nominal rate + frequency into the true yield.
Strip inflation out to see real buying-power growth.
How a small annual fee compounds against you over decades.
Every chapter of this book links to a calculator on this page; the full list is on the book’s page. One is new:
Every chapter of this book links to a calculator; the full list, with the worked examples, is on the book’s page. These are new:
A grade whose parts count differently, and what you need on the last part.
Mean, median, quartiles, standard deviation, outliers, histogram and box plot.
How unusual is a value? Its z-score, percentile and equivalent on another scale.
What a raffle, bet or warranty pays back on average.
Roll thousands of dice and watch averages turn into a bell curve.
The share above, below or between values, or the cut-off for a share.
A fair random sample from any numbered or pasted list.
A poll’s margin, the margin on a lead, and the sample you need.
A range for the true average, with Student’s t for small samples.
The exact p-value for successes in a number of tries.
Two conversion rates: difference, interval, p-value and power.
What a positive result really means when the thing is rare.
Scatter plot, r, r², least-squares line, residuals and predictions.
Every chapter of this book links to a calculator; the full list, with the worked examples, is on the book’s page. These are new:
What the same change in price, sales or cost does to profit.
Split a mixed cost from a quiet period and a busy one.
Rank products by contribution and by what is scarce.
Break-even, a target profit, the margin of safety and a new price.
The rate you need from the hours customers actually pay for.
The extra sales a cut needs, the sales a rise can lose, stacked discounts.
Margins, every line as a share of sales, and this year against last.
From a period’s profit to the change in cash, step by step.
Days of stock, days to get paid, days before you pay, and cash freed.
Equity, current and quick ratios, debt to equity and returns.
Straight-line depreciation and the cost per hour of use.
Changes, CAGR, monthly compounding and real growth.
What one order leaves, and the smallest order that pays.
Churn, lifetime value, acquisition cost and the customer ceiling.
Today’s value of future amounts, NPV and IRR.
Price and volume variances and a flexed budget.
Billed hours, the bottleneck, and overtime against a part-timer.
How funnel steps multiply, and how the sales mix moves a margin.
Every chapter of this book links to a calculator; the full list, with the worked examples, is on the book’s page. It also uses Dice Lab, Base Rate and Expected Value above. These are new:
Any chance as a percentage, “1 in”, odds, and per day, year or lifetime.
Combinations and arrangements, and the chance of hitting one.
Repeated chances, and the tries you need for an even or 90% chance.
Every “given” chance from a table of counts, both ways round.
A million dice settling on one in six, 60% heads, and a wheel’s house edge.
Shared birthdays, or a shared anything, in a group of any size.
A one-in-ten-thousand day, for you and for a whole town.
The exact chance of a run, the average longest run, and a coin to flip.
Stick or switch? Play by hand or a thousand rounds at a time.
How many perfect records a crowd produces by luck alone.
Best guess next time, and a league of equally good players.
Every prize’s chance, and what a ticket is worth on average.
Price per dollar of cover, break-even, and which excess is cheaper.
“Doubles the risk” as counts per 10,000 and the number needed.
A yearly or per-trip risk over a lifetime, exactly.
Reaching a target before going broke, swings and doubling systems.
Change your mind by the right amount: odds × evidence ratio.
Average waits, yearly risks, random arrivals and collecting a set.
Chains, backups, two-out-of-three voting and shared causes.
One calculator for each chapter, each opening on the book’s own worked example, all with exact fraction arithmetic. The full list, with the worked examples, is on the book’s page.
Any fraction as bars and a pie, mixed numbers, and a fraction of an amount.
Which is bigger, by how much, and lowest terms.
Add and subtract fractions and mixed numbers over a common bottom.
Multiply fractions and scale a recipe to any number of people.
How many fit, why you flip, and what the leftover is.
Decimals to fractions and back, with place value.
Multiply as whole numbers, then count the places back.
Every step, whether it ends, and a bill split to the cent.
Round any way, split so the pennies add up, and round up when you must.
Type one, see all three and a hundred-square.
Any percentage of any amount, built from 10%, 5% and 1%.
The price before the discount or tax, and what percent it is.
Change, points, multipliers and the change that undoes it.
Discounts, taxes, coupons and compounding, step by step.
Share any total in a ratio, as amounts, fractions and percents.
Per item or per sheet, and fuel savings in gallons.
Scale anything, with fixed parts and inverse proportion.
Areas, price per square inch, pans and enlargements.
A rough answer beside the exact one, to catch slips.
Bills, rent, nights and settling up, fairly.
Weighted grades, blends and the score you need next.
One tool for each chapter, each opening on the book’s own worked example and drawing the method the way your child is asked to draw it. The full list, with the worked examples, is on the book’s page.
What a worksheet method is called, in the US and the UK, and where it’s explained.
Base-ten blocks, expanded form and renaming a number.
Ten frames, part-whole models and fact families.
Add and subtract in jumps; count up, count back.
Partial sums, carrying and exchanging, step by step.
Any fact as an array, with the strategies that build it.
The box method, partial products, the standard algorithm and lattice.
Chunking, the bus stop, long division and remainders.
Equal fractions, ordering and a fraction of a group.
Same-size pieces, mixed numbers and counting up.
Multiply and divide fractions with pictures.
Hundred grids, lining up the point, the digits moving.
Any word problem as a bar model, with the steps.
Missing numbers, true or false, order of operations.
On a number line, with the checks that catch slips.
Time on a number line, clocks and counting up change.
Rectangles, L-shapes and boxes of cubes.
Keys, scales, totals and the mean.
Gentle practice, one strategy family at a time.
Ten frames, hundred charts, number lines, squared paper and more.
One calculator for each chapter, each opening on the book’s own worked example. The full list, with the worked examples, is on the book’s page.
Percent off, factor off, and whether it’s close enough.
Round, see how far it moved, and balance a product.
Count the zeros; multiply and divide by powers.
Millions and billions as time, stacks and per person.
Multiply digits, add zeros; divide by a friendly number.
Split a big question into factors you can guess.
The numbers worth carrying, and any rate in any unit.
Low, high, and the ladder middle between them.
Why rough guesses multiplied together land close.
Conversions as a chain of factors that cancel.
Daily minutes to yearly hours, lines and to-do lists.
Pack vs single, × 365, × 2,000 and the rule of 72.
Paces, mulch, paint, water and boxes.
Crowds by area, visits over a day, samples scaled up.
Rule of 72 against the exact time, and doublings counted.
Spread a claim over people, days and minutes.
Six checks for numbers that can’t be true.
Add and multiply ranges; see if two overlap.
Low, likely, high, corrected by your track record.
Top-down and bottom-up, the middle, per person.
Walk the world, light to the Moon, the weight of the air.
Take-home − savings − bills − debt − discretionary = surplus.
Split take-home by percentage — and check the shares hit 100%.
Yearly and occasional bills → the monthly amount to set aside.
Budget on the floor, bank the good months, build a reserve.
Debt ÷ take-home, your ceiling, headroom, and does-a-loan-fit.
Saved ÷ take-home, the gap to target, pay-yourself-first.
Variable cost plus a fair share of fixed costs = the real cost of one unit.
Flip between the two, and price to a target margin.
True cost + target margin → the price, and the floor you can't cross.
Fixed ÷ contribution = units to sell, revenue, and margin of safety.
How long your cash lasts at your monthly burn.
Park the right share of profit — you pick the rate.
New contribution and the extra volume a markdown really needs.
Payout − costs ÷ every minute (active + wait + drive + admin) = your true rate.
Listing + commission + payment + withdrawal — see what actually lands.
Miles × per-mile rate — the honest running cost of your car.
Four rough tests — regularity, motive, scale, presentation.
Work backwards from what you want to keep to the price to send.
Marginal hourly of the next hour vs its honest opportunity cost.
How many extra sales the boost must truly cause to pay for itself.
X% of a number, X is what % of Y, and percent change from one figure to another.
Add, subtract, multiply, or divide two fractions — mixed numbers supported. Result reduced.
A 30, 60, or 90-second timed round of shortcut-friendly problems, with scoring at the end.
Solve a : b = c : d for any missing term, or scale a recipe from N servings to M.
Type a·x + b = c and see each isolation step, plus a check on the answer.
Length, weight, volume, and temperature — metric and US customary, exact factors.
Paste a list of numbers and get all four at once, with a short explanation of each.
Convert hourly ↔ weekly ↔ biweekly ↔ monthly ↔ annual, plus overtime and take-home.
Take-home − savings − bills − debt − discretionary = surplus, on one page.
Lump sum + monthly saving compounded; growth vs what you actually put in.
Months to zero, total interest, and avalanche-vs-snowball ordering for several debts.
Price ÷ quantity across items — the pack that's genuinely cheaper per unit.
Your own bands → tax, effective rate, and the marginal rate on your next dollar.
Fixed costs ÷ contribution per sale — the point where a decision pays its own way.
Add, subtract, multiply or divide two fractions — mixed numbers in, reduced fraction out.
Cups, tablespoons, teaspoons, millilitres, grams, ounces, and °F ↔ °C with exact factors.
Scale by servings; amounts come back as kitchen fractions, salt and leaveners held back.
Correct the label for what you really ate, cross-check the 4-4-9 macros, compare per 100 g.
Price ÷ quantity across items — the can, jar or bag that's genuinely cheaper per unit.
Work backwards from serving time to a start time per dish; convert the oven dial both ways.
Timed practice on the halving, doubling and 10% shortcuts the chapter teaches.
Add rectangles, triangles and circles, subtract the patio and pond, get net growing area.
Cubic feet, cubic yards and bag counts, then bags priced against a bulk delivery.
Rows, plants per row, the square-foot cross-check, and seeds to buy at your germination rate.
Work back from the jars you want to the plants you need, waste allowance included.
Frost dates to season length, seed-starting dates and a succession-sowing schedule.
Gallons a pot holds, its weight when wet, and whether the balcony can take the load.
Timed practice on the estimation shortcuts the chapter teaches.
Convert either way, price back from a target margin, and see what a discount really costs.
Change between two values, several changes chained, and points kept apart from percent.
Break-even in units and revenue, and what moves it when price or cost shifts.
Walk a gross figure down through tax, FICA, insurance and retirement to take-home.
The same numbers on an honest axis and a truncated one, so you can see the real gap.
All four at once, outliers flagged, and weighted averages done properly.
Return, payback period and the trade-off between them, for one option or two.
Net profit + depreciation − rise in receivables + rise in payables = operating cash.
Confirm the wires agree — profit to equity, and ending cash to the balance sheet.
The six looks in order, then hunt the four first tells on any set of accounts.
Paste a set of figures and see whether the leading digits climb the natural staircase — or break it.
Drop in a run of monthly returns and see how suspiciously flat they are next to a real market.
The Detective's Fast-Scan — nine ratios and the numbers each one is trying to tell you.
Annualise any monthly return, run the rule of 72, and see whether a "12%/month" pitch is even possible.
List every recurring charge and see the annual damage. The small leaks add up faster than you think.
Turn a "$45 fee for two weeks" into an APR, and a "cheap monthly" into what it actually costs.
Board feet and cost, nominal vs. actual, whole shopping lists of boards.
Kerf-aware nesting: parts in, strip layout and yield out.
Diagonals in, lean out; scales a 3-4-5 to any legs.
Divides a span, with running positions to mark from one end.
Every joint from one stock thickness, plus side-grain glue area.
Saw setting for any n; long point ↔ short point at any angle.
Two splays in, resultant, sightline, both saw settings, leg length.
Deflection, with the span ÷ 360 line marked.
Cabinet dimensions → surface area → litres.
Coverage and solids → wet film, dry film, coats, spray passes.
The whole roll-up, and the four-line ledger.
The resistor to fit, the one you can buy, and the current you really get.
Series and parallel packs, a usable derate, and the C-rate a load asks for.
The one to bookmark. Every line of your design, and its share of the battery.
Output, loading, source impedance, and the yearly bill if nobody switches it off.
What one step is worth — and why fine is not the same as true.
Slope and offset from two known points, and an error bar you can defend.
How long to wait before reading, and what the waiting costs.
What a load costs per year once you say how long it is connected.
A quarter of the current does not buy a quarter of the light.
The two bills a regulator sends, and buck against linear for your interval.
Which runs out first, the battery or the memory — and what a radio costs.
Runtime when the world decides how often, plus stall current.
Measure a current your meter cannot read, then explain the gap.
Any two of volts, milliamps, ohms and milliwatts — and the other two.
Combine resistors, and find the E12 value you can actually buy.
Cells in series and parallel — volts, usable mAh, and days.
Runtime at every interval, and where waking less often stops paying.
Readings past a line, turned into hours below freezing or above damp.
The unit conversions every battery sum in the book turns on.
The range a cup recipe really covers — not one flattering number.
Formula to grams for any dough weight, with a misprint check.
Read it, change it, and put a too-wet dough right — salt and yeast included.
The dough your pan wants, and the factor between any two pans.
The final mix with nothing counted twice, and a feed by ratio.
The water sum, then the grams of kettle, tap and ice to make it.
From when you want to eat to when you must start — across midnight.
Dough for a promised weight, baguettes by length, overlapping cuts.
°C, °F, gas mark and fan with your oven's offset, and the electricity.
Butter, egg and honey replaced — and the water each swap adds.
Layers for any folds, the fat block, and a sheet cut into triangles.
What a bake costs, what a price leaves, and a market day added up.
The one to bookmark: four formulas sized to your pan, on one sheet.
Net area, coats and coverage rate in — litres, the tin to buy, and the leftover.
Two widths and a depth in — true area, order area, and how far out of square you are.
Area, waste % and a pack's coverage in — whole packs to buy, and the real spare.
Span and board width in — full rows and a matched edge row each side, never a sliver.
Span and centres in — batten count, then screws per m² for a whole wall.
Area and thickness in — bags to buy, plus a tile-by-tile grout calculator.
A 500 mm arm-check in — the real corner angle and the mitre setting.
A door leaf in — lining, structural opening, architrave, fixing depth, window board and blind.
Floor build-up against a door gap, furniture against a walkway, a room drawn to scale.
Gross and tax rate in — the net figure, honestly, plus two quotes compared.
Materials and a builder's quote in — the saving, and what your time was worth.
Any wall, any block or brick, counted two ways — joint included, waste added, cuts flagged.
3-4-5 diagonals, a rectangle checked, a fall turned into a slope, and footing steps.
Dig, pour, and the real choice: 77 heavy bags or one small truck.
Cost per meter, and cost per meter per year of life, for every route you price.
Bags, the same answer by volume, mix-your-own, and the right batch size.
The square law, the published bar spacing, and the grout to fill the cores.
½ρgh² per meter, where it acts, and the push on a whole wall and a gate.
A flood wall keeps rain in too: liters an hour, and whether the pump keeps up.
Both faces and the ends: bags of base and finish coat, and gallons of paint.
Quantity, waste, order, price and total for every material.
Saturday and Sunday, hour by hour, with the waits written in.
The line, the 3-4-5 corners and the fall of the ground.
Bays and posts for any run, open or closed, with the real spacing and a gate.
Post centers from one zero, 3-4-5 corners at any size, and the slope as a percent, an angle and inches per foot.
Post length, hole volume, bags of concrete per hole and in all, gravel, and the weight you are moving.
Every fence type by cost per foot and per meter, and cost per year with your own life estimate.
Equal gaps between posts or on a gate, the picket count for a target gap, and boards on a long run.
Racked or stepped: the fall per bay, rail length and cut angle, and the triangles under a stepped panel.
Wind pressure by speed, the push on one post, and what spacing and height do to it.
Gate width from the opening, the brace length and angle, the gate's weight and the pull on the top hinge.
Area to finish, gallons for your coats, and the cost per year of each kind of finish.
Quantity, spare, order, price and total for every material.
Two weekends, job by job, with the waits for concrete and stain written in.
The line, post centers from one zero, a 3-4-5 corner and the cutting list.