Tip: bookmark or share a direct link to one tool with a hash in the URL (for example free-tools.php#loan or free-tools.php#paint). The index at the bottom lists the same anchors.
Calculator
Good for: shopping totals, simple budgets, scaling measurements, or checking homework—anything that needs several steps in one go (no “scientific” brackets).
How to use: enter each amount in the list (like a tape), pick the operation before each value after the first, then = Calculate. Add number adds another step; Remove drops a row if you duplicated one. Calculations run left to right (e.g. 2 + 3 × 4 = 20). Each time you calculate, a line appears in History — use Edit in calculator to reload that run, fix a figure, and recalculate.
How to do these sums on paper
Work one step at a time from left to right (same order as this page).
- Add (+): stack the numbers by place (units under units, tens under tens), add each column, carry if a column is 10 or more.
- Subtract (−): same layout; if the top digit is smaller, borrow 1 from the column to the left, then subtract.
- Multiply (×): treat as “lots of” — e.g. 6 × 40 = 6 × 4 tens = 240. For decimals, count total decimal places in the factors and put that many in the answer.
- Divide (÷): “how many times does the bottom number fit into the top?” For a rough check, multiply your answer back by the divisor — you should get the original (allowing small rounding).
Unit converter
Good for: DIY and materials (mm ↔ m ↔ ft), cooking weights, luggage ideas, room sizes, and temperatures abroad—whenever a label uses a unit you do not think in.
How to use: pick a category, type the amount in From, and read every common equivalent below. Preferred unit puts that column first; your category and preferred unit are saved on this device. When a Pack price & project section appears (same category), use it to compare a shop pack size to how much your job needs.
How to convert units by hand
Every conversion is “multiply or divide by the link between the two units.”
- Find the bridge. Example: 1 mile = 1.609 km (fixed). 1 kg = 2.205 lb (approx).
- Metres → centimetres: multiply by 100 (there are 100 cm in 1 m).
- Centimetres → metres: divide by 100.
- Big → small unit = multiply. Small → big unit = divide. (More of the smaller unit fits in one big unit.)
- Temperature: °C to °F:
F = (9/5) × C + 32. °F to °C:C = (F − 32) × (5/9).
Currency converter
Good for: rough trip budgets, comparing an overseas price to home, or ballparking an invoice in another currency—not for exact bank settlement.
How to use: enter the amount, choose From and To currencies, then Convert. Use Refresh rates if the page has been open a long time. Rates are mid-market style from the free ExchangeRate-API (refreshed on their schedule, often about daily). Your card or bank may apply a different rate or fee—check with them before you move money.
How to convert currency on paper
You need one rate: “how many units of currency B for 1 unit of currency A?” (e.g. 1 GBP = 1.27 USD).
- A → B: multiply your amount in A by the rate. Example: £50 × 1.27 = $63.50.
- B → A: divide by the rate (or multiply by 1 ÷ rate). Example: $63.50 ÷ 1.27 ≈ £50.
- Check: banks often use a slightly different “tourist” or card rate — this page uses a public mid-market style rate for estimates only.
Area from common shapes
Good for: turf, carpet, decking, fabric on a rectangular piece, circular patio slabs, or any quote that asks for area in m² or ft² from sizes you can measure.
How to use: choose the shape that matches your job, enter every field it asks for in one length unit (all metres or all feet, for example). The answer and a small diagram update from your inputs. Open Material cost below when you want pack or tile prices from that area.
How to work out these areas by hand
Use the same length unit for every side before you plug numbers in (all metres, or all feet, etc.).
- Rectangle: area = width × height.
- Circle (radius r): area =
π × r². Circumference =2 × π × r. Use π ≈ 3.14 for a rough answer. - Triangle (base b, height h): area =
½ × b × h(half of a matching rectangle). - Triangle (three sides a, b, c): first check each pair sums to more than the third side. Then Heron:
s = (a+b+c)/2, area =√(s(s−a)(s−b)(s−c)). - Trapezoid (parallel sides a, b, height h): area =
½ × (a + b) × h— average width times height. - Parallelogram: area = base × perpendicular height (not the slanted edge unless it’s truly vertical to the base).
Material cost (tiles / packs) from this area
The number from “Area: …” is copied into “Project area” when you click the button—then pick which unit that number is in (same as your shape dimensions, e.g. m² if sides were metres). Pack price can be per box of tiles: either enter area one pack covers or tile width × length in any mix of length units (mm, cm, m, ft, …).
How to estimate packs and cost by hand
- Put project area and area per pack in the same unit (convert with length² rules: 1 m² = 10,000 cm², etc.).
- Packs before waste ≈ project area ÷ area per pack. Add waste: multiply by
1 + waste%/100, then round up to whole packs. - From tile size: one tile’s area = width × length (same units). If a pack has
ntiles, pack area ≈n ×that area. Then same steps as above.
Triangle solver
Good for: site surveys, carpentry cuts, school geometry, or checking a roof or bracket shape when you only know a few measurements.
How to use: under Known, pick the option that matches your tape measure (three sides, two sides plus the angle between them, or angles plus a side). Fill in the boxes in one unit system, then press Solve. You get missing sides, angles, and area where the numbers can form a real triangle.
How to solve triangles with pencil & paper
Angles in a flat triangle always add to 180°. Label corners A, B, C and the side opposite each as a, b, c.
- Three sides (SSS): use the cosine rule to get an angle, e.g.
cos A = (b² + c² − a²) / (2bc), then inverse-cos on a calculator. Repeat for other angles, or subtract from 180° once you have two. - Two sides + angle between (SAS): missing side from cosine rule:
a² = b² + c² − 2bc cos A, then square root. - One side + two angles (ASA / AAS): find the third angle (180° minus the two you know). Then sine rule:
a / sin A = b / sin B = c / sin C— pick a pair to solve the next side. - Area from three sides: Heron’s formula (same as Area tab): semi-perimeter
s, then√(s(s−a)(s−b)(s−c)).
Circle solver
Good for: round tables, tree trunks, pipe sizes, garden beds, or any disc where you measured one of radius, diameter, circumference, or area.
How to use: type any one of radius, diameter, circumference, or area (leave the others blank). The rest fill in automatically—stick to one real-world unit (e.g. all cm or all m) so the diagram and numbers stay consistent.
Use consistent units (e.g. all metres). π used internally with double precision.
How circle formulas link together
- Diameter
dis twice the radius:d = 2r. - Circumference (distance round the rim):
C = πd = 2πr. Wrap a string round a can, measure the string — that length ≈ C. - Area of the disc:
A = πr². Rough check: count how many “radius squares” fit in the circle — it’s always about 3.14 of them (π). - If you know only C, then
r = C / (2π), then you can getAfromr.
Custom closed outline (e.g. room)
Good for: L-shaped or odd rooms, quick site sketches, and “how much floor” when a simple rectangle is not enough. The pad below is the same Room layout draw engine as the signed-in lite planner (walls in mm; area and perimeter update when you close the outline).
Draw in the pad: use the Draw tool on the dock, click corners, then snap closed on the green start (Shift / Ctrl and wheel zoom behave like the full tool). Switch Select or Edit to move corners. Nothing is saved to your account here. Open this sketch in a new tab · Signed-in users: Room layout (lite) for the same experience with header navigation.
For Material cost from outline area below, pick m² as the project area unit so it matches the numbers from the sketch (shown in m²).
How plan area & perimeter are worked out
Your sketch uses plan units (whatever one grid unit means — often 1 unit = 1 metre).
- Perimeter (open or closed): add the lengths of every drawn edge. For a closed room, that’s the total distance round the walls.
- Area (closed shape only): the tool uses the shoelace idea: list corners in order around the shape, repeat the first at the end, then sum “down-right products minus down-left products” and take half the absolute value. (Doing it on graph paper with corners on known grid points is the easiest manual check.)
- Angles at corners: in a simple polygon they sum to
(n − 2) × 180°forncorners — a quick sanity check for manual surveys.
Material cost from outline area
When the outline is closed, use the computed plan-area number as your floor size (choose its unit). Mixed tile units supported (e.g. width in mm, length in cm).
Outline area is in the same plan units as your edge lengths (whatever real-world length one drawing unit represents—often metres). The project area unit dropdown should match that convention so pack coverage and cost stay correct.
Manual check (same as Area tab packs)
Use the outline’s area number as “project area,” then: match units to each pack’s coverage, divide, add waste %, round up; total cost ≈ number of packs × pack price. The logic is identical to the shape area material box above.
VAT / sales tax (add-on %)
Good for: quick checks on quotes and receipts—turning a net price into gross (with tax) or stripping tax off a total to see the net. Default 20% matches common UK VAT; change the rate for other countries or reduced rates.
How to use: set the Rate (%), then enter either Net amount or Gross amount (leave the other empty). The tool fills in tax and the missing total. Illustrative only—real rules can depend on what you sell and where; use an accountant for compliance.
How to add or strip VAT on paper
Treat the rate as a fraction of 100 — e.g. 20% → 0.20.
- Net → gross: tax = net × (rate ÷ 100). Gross = net + tax. Shortcut: gross = net × (1 + rate/100). Example: £100 + 20% → £100 × 1.20 = £120.
- Gross → net: net = gross ÷ (1 + rate/100). Example: £120 ÷ 1.20 = £100.
- Tax only from gross: tax = gross − net, or tax = gross × (rate ÷ (100 + rate)). For 20%: tax = gross × (20/120).
Margin & markup
Good for: retail and trade pricing—seeing whether a sell price covers stock cost, or working backwards from a target margin on sell (what many accountants mean by “margin”).
How to use: enter Cost and Sell price to see profit, margin %, and markup %. Optionally add Target margin % on sell with cost filled in to get a suggested sell price. Margin % is profit ÷ sell; markup % is profit ÷ cost—they are not the same number at the same price.
How margin and markup differ on paper
- Profit (money): sell price − cost.
- Margin % (share of selling price): margin = (sell − cost) / sell × 100. Example: cost £50, sell £80 → profit £30 → margin = 30/80 × 100 = 37.5%.
- Markup % (share of cost): markup = (sell − cost) / cost × 100. Same example: 30/50 × 100 = 60%.
- Sell from cost + target margin % on sell: sell = cost ÷ (1 − margin/100). Example: 40% margin, cost £60 → sell = 60 ÷ 0.60 = £100.
Loan payment (amortising)
Good for: ballparking car loans, personal loans, or hire-purchase style deals with a fixed APR and the same payment every month until paid off.
How to use: enter Principal (amount borrowed), APR % (annual rate), and Term in years. Results update as you change figures. Illustration only—lenders add fees, different day-count rules, or variable rates; this is not an offer of credit.
How a fixed monthly loan payment is figured out
You borrow P, pay every month for n months, annual rate R%.
- Monthly rate:
i = (R / 100) / 12. - Payment (standard formula):
M = P × i × (1+i)n / ((1+i)n − 1). On paper people use a calculator for the powers; the idea is each month you pay interest on what you still owe, then the rest chips away at the balance. - Quick sense-check: if there were no interest, you’d pay about
P / nper month — real payments are higher because of interest.
Date & duration
Good for: notice periods, rental gaps, project timelines, warranty “30 days from purchase,” or “what date is 45 days after signing?”
How to use: pick a start and end date to see how many days lie between them (calendar days). Or keep the start date and type a number in Add days to start to get the calendar date that many days later.
How to count days between dates by hand
- Calendar method: count whole days from the day after the start date up to and including the end date (or match whatever rule your contract uses — some count both ends, some exclude weekends).
- Add days to a date: add to the day number, then carry into months using how many days each month has (30/31; February 28 or 29 in a leap year — leap years are divisible by 4, except centuries unless divisible by 400).
- Julian day (advanced): convert both dates to a single day count, subtract — that’s what programs do under the hood.
World time zones
Good for: scheduling calls with clients or family abroad, checking “is it still office hours there?”, or lining up a release time with another country.
How to use: type a city or region in Add region, pick from the list, then Add. Your device clock drives “now”; standard IANA zones (e.g. Europe/London) handle daylight saving correctly. Remove last drops the last row; Reset defaults restores a starter set. Your list is saved in this browser. Times tick every second while this tab is open.
How to compare two time zones on paper
Each zone is “UTC (GMT) plus or minus an offset.” Daylight saving shifts that offset part of the year.
- Write both cities’ current offsets from UTC (e.g. London winter = UTC+0, New York winter = UTC−5).
- Difference between offsets = hours you add or subtract when converting. Example: UTC+0 to UTC−5 → New York is 5 hours behind London.
- Same moment: start from one local time, add the difference (with sign) to get the other — then fix if you cross midnight.
Fuel trip cost
Good for: “roughly what will this drive cost?” before a long trip, or comparing two cars using their consumption figures.
How to use: choose Units (UK: km + L/100 km + price per litre; US: miles + MPG + price per gallon), then fill distance, consumption, and local pump price. The estimate updates from your inputs—actual traffic and driving style will change real use.
How to work out trip fuel cost by hand
- Metric (L/100 km): litres used = distance × (L/100 km) ÷ 100. Cost = litres × price per litre. Example: 200 km at 7.5 L/100 km → 200 × 0.075 = 15 L; at £1.45/L → £21.75.
- US (MPG): gallons = miles ÷ MPG. Cost = gallons × price per gallon.
- Convert MPG ↔ L/100 km:
L/100 km = 235.214583 ÷ MPG(approx). Higher MPG means lower L/100 km.
Percent helpers
Good for: exam-style “what percent is this of that?”, sale prices after a discount %, or reporting growth between two numbers.
How to use: pick a Mode—Part of whole needs A and B; % change needs old and new values in A and B; Price after discount needs price and discount %. Labels under the inputs change to match.
How to do the % modes on paper
- “Part is what % of whole?” divide part by whole, then × 100. Example: 25 of 200 → 25/200 = 0.125 → 12.5%.
- “% change from A to B”: change = (B − A) ÷ A × 100. If A is 80 and B is 100, that’s +25%.
- “Price after discount”: pay
price × (1 − discount/100). Example: 15% off £40 → £40 × 0.85 = £34.
Average (mean)
Good for: class grades, repeated measurements, sample costs, or any set of numbers where you want the usual “add them up and divide by how many” average.
How to use: type each value on its own row. Add value adds another row (as many as you need, up to the limit). Remove deletes a row if you typed one twice or do not need it. Blank rows are ignored when you press Calculate average so you can leave spare lines empty.
Average: —
How to average on paper
- Count how many numbers you are including (ignore blanks).
- Add them all to get the total (sum).
- Divide the sum by the count — that is the arithmetic mean (average).
- Example: 12, 18, and 24 → sum = 54, count = 3 → average = 54 ÷ 3 = 18.
Paint quantity (tins)
Good for: decorating one room when the tin says “covers X m² per litre” and you know how many coats you want—so you do not buy three tins when one would do (or the opposite).
How to use: either tick Use area directly and type wall/ceiling area in m², or leave it off and enter width × length for a simple rectangular floor plan of the painted surface. Add coats, the can’s coverage (m² per litre), and tin size (L). The answer rounds up to whole tins; allow extra if you have big windows or strong colours.
How to estimate paint volume and tins
- Wall area: add each rectangle (width × height). Subtract big windows/doors if you want a closer guess.
- Paint needed (litres of liquid): (area × coats) ÷ coverage (m² per litre). Example: 20 m², 2 coats, 12 m²/L → (20×2)/12 ≈ 3.33 L.
- Tins: divide litres by tin size, then round up to whole tins — leftover is better than a short final coat.
Roof pitch & slope
Good for: matching an existing roof pitch, briefing a builder (“6 in 12”), or converting between ratio, degrees, and percent grade (useful for ramps and drives too).
How to use: enter rise and run in the same units (e.g. both inches, or both cm)—the ratio is what matters, e.g. 6 : 12. Read off angle and grade; tweak rise or run to see how steep the slope becomes.
How pitch, angle, and grade relate
- Rise : run (e.g. 6 : 12) means “up 6 for along 12” in the same length units — it’s a ratio, not inches-by-itself unless you chose inches for both.
- Angle θ (degrees):
tan θ = rise / run→ θ = inverse-tan on a calculator. - Percent grade:
(rise / run) × 100— same as “rise per 100 units of run” when run is horizontal distance.
Invoice line (ex-tax + tax)
Good for: freelancers and small shops checking a single invoice line—quantity × unit price, optional line discount %, then VAT/sales tax on the discounted line (common UK-style “ex-VAT” wording).
How to use: all prices are excluding tax until the last step. Enter quantity, unit price (ex tax), any discount % for that line, and the tax rate %. Read line subtotal, tax, and line total including tax.
How an ex-tax invoice line adds up
- Line before discount: quantity × unit price (both ex tax).
- After discount %: multiply by
(1 − discount/100), or subtractline × discount/100. - Tax on that discounted line: tax = discounted line × (tax rate ÷ 100).
- Total including tax: discounted line + tax (same as discounted line × (1 + tax/100)).