Cheatsheet

Packages: this page spans every built-in. createEngine() registers them all; for a slimmer engine, register just the packages the features you use need (each syntax page names its own, see choosing packages).

A map of the syntax reference. Every area of the language has a line or two here that you can edit in place, and a link to its own page, where the form is explained in full. This page is for scanning: the explanations, the variations and the edge cases stay on the pages it links to. The areas are grouped the way the sidebar groups them.

Every example below is executed against the engine when the documentation is built, so if one of them is wrong the build fails rather than the page quietly going stale. The few areas whose answers come from the network, or from a function the host application supplies, have no fixed answer to check, so they are named in text rather than shown as a live line.

Writing a note

A note is a column of lines, and each line is worked out on its own unless it reads another. Text after // is a comment the engine skips. A line starting with # is a heading: it gives no answer, and it names a section.

2 + 2 // comment // 4

Labels: words that name a line’s figure, kept as text while the rest is worked out, before a colon or, when an amount of money or a quantity ends the line, without one.

total: 5 + 3 // 8
Rent $1200 // $1,200.00

Arithmetic

Operators: add, subtract, multiply, divide and raise to a power, in symbols or in words, with multiplication done before addition. % means percent, so the remainder after a division is mod.

2 + 2 * 10 // 22
10 plus 5 times 2 // 20
17 mod 5 // 2

Number suffixes: a letter after a number as shorthand for thousands (k), millions (M), billions (B) and trillions (T).

2.5k // 2,500
3M // 3,000,000

Decimals: a number with a decimal point is kept as the exact decimal you typed and worked in base ten, so 0.1 + 0.2 is exactly 0.3 rather than a near miss.

0.1 + 0.2 == 0.3 // true

Fractions: a quotient of whole numbers stays exact, and as fraction shows it as one.

1/3 + 1/3 + 1/3 // 1
10/4 as fraction // 5/2

Percentages: a percentage of a number, a discount or a markup, the change from one value to another, and the whole a percentage was taken from.

10% of 250 // 25
15% off 80 // 68
100 to 150 // 50.00%
5% of what is 6 // 120

Ratios: a ratio reduced to its lowest whole-number terms.

ratio(1920, 1080) // 16:9

Rounding: to a number of decimal places (dp), in a chosen direction, or to the nearest ten, hundred or other step.

round(3.14159, 2) // 3.14
3.14159 to 4 dp // 3.1416
-25 to nearest 10 // -30

Number functions: everyday maths functions such as the square root, the absolute value (the size of a number without its sign) and the greatest common divisor (the largest number that divides both).

sqrt(16) // 4
abs(-5) // 5
gcd(12, 18) // 6

Uncertainty: a measurement with a tolerance, written +/-, carried through the arithmetic so the answer says how far it can be trusted.

(12.3 +/- 0.5) * 4 // 49.2 ± 2.0

Conditionals: comparisons that answer true or false, and, or and not, and if ... then ... else.

10 == 10 // true
not (1 > 2) // true
if 5 > 3 then 100 else 200 // 100

Numbers

Numerals: a number written out in words, as an ordinal (1st, 2nd, 3rd) or in Roman numerals.

1234 as words // one thousand two hundred and thirty-four
3 as ordinal // 3rd
2024 as roman // MMXXIV

Big integers: whole numbers past 9,007,199,254,740,991, where an ordinary floating-point number starts to drop digits, stay exact; the n suffix writes one directly.

2^53 + 1 // 9,007,199,254,740,993
123n * 2 // 246

Primes, factors and counting: testing whether a number is prime, breaking it into its prime factors, and factorials (5! is every whole number from 1 to 5 multiplied together).

isprime(97) // true
factor(360) // 2^3 * 3^2 * 5
5! // 120

Complex numbers: numbers with an imaginary part, written with i (the square root of -1), which is what the square root of a negative number needs.

sqrt(-4) // 2i
(1+1i)*(1-1i) // 2

Constants: named physical and mathematical constants, carrying their units.

speed of light // 299,792,458.00 m/s
gravity * 70 kg as N // 686.47 N

Programmer math

Number bases: numbers written in hexadecimal (0x), binary (0b) or octal (0o), and shown in any of them with as.

0xFF // 255
255 as binary // 0b11111111

Bit shifting: moving the bits of a whole number left or right, which multiplies or divides it by a power of two.

1 << 8 // 256

Bitwise operators: and, or, exclusive or (xor) and complement, applied to each bit of a whole number.

0xFF & 0x0F // 15
12 xor 10 // 6

Data sizes: bytes and bits, with the decimal prefixes (a kB is 1,000 bytes) kept apart from the binary ones (a KiB is 1,024), and how long a download takes at a given speed.

1 KiB in bytes // 1,024.00 bytes
4 GB at 50 Mbps // 10.67 min

Algebra

Expanding: multiplying out brackets and collecting the like terms.

expand((x+1)*(x+2)) // x^2+3x+2

Factoring: writing a polynomial as a product of simpler factors, the reverse of expanding.

factor(x^2-4) // (x-2)*(x+2)

Solving equations: the values of an unknown that make an equation true, exactly where there is a method and numerically where there is not.

solve(x^2-4=0, x) // [-2, 2]
solve(cos(x) = x, x) // 0.74

Cancelling a fraction: a fraction of polynomials reduced to its lowest terms.

cancel((x^2-1)/(x-1)) // x+1

Splitting a fraction: a fraction of polynomials broken into the simpler fractions that add up to it (partial fractions).

apart((3x+5)/(x^2-1)) // 4/(x-1)-1/(x+1)

Exact coefficients: the numbers in front of the terms of a symbolic expression (its coefficients) stay exact fractions, so they pick up no floating-point error.

0.1x + 0.2x => // 0.3x

Calculus: derivatives (rates of change), integrals (areas under a curve), limits, Taylor series and Jacobians.

der(x^3, x) // 3x^2
integral(x^2, x, 0, 3) // 9

Symbolic: a letter with no value stays an unknown rather than an error, and => at the end of a line asks for the simplified expression.

1+2+x+3+x => // 2x+6

Statistics

Vectors & matrices: lists of numbers in square brackets, with ; between the rows of a matrix, worked on element by element or with linear algebra.

[1,2,3] * 10 // [10, 20, 30]
det([1,2;3,4]) // -2

Map, reduce & aggregates: a range written start:end, an expression applied to every item of a list, and a list folded down to one value. A range is read only inside brackets or a function call, since a bare 0:3 is a clock time.

map(10*x, 0:3) // [0, 10, 20, 30]
sum(x, 0:4) // 10
reduce(acc+x, [1,2,3]) // 6

Statistics: averages, medians, totals and other summaries of a list, in plain phrasing.

average of 10, 20, 30 // 20
median of 1, 5, 3 // 3
half of 50 // 25

Probability distributions: the normal, binomial, Poisson and Student’s t distributions, for the chance of a result and the result for a chance.

normalcdf(1.96) // 0.98
binompdf(10, 0.5, 3) // 0.12

Finance

Currency: money written with a symbol, a code or a word. Converting between currencies, as in 10 USD in GBP, uses live exchange rates, so it has no fixed answer to show here.

$100 + $50 // $150.00
10 dollars // $10.00

Money precision: money is held as an exact decimal, so a column of prices adds up to the cent instead of drifting by a fraction of a penny.

$0.10 + $0.20 // $0.30
$10 / 3 // $3.33

Tax: adding tax to a price, taking it off a total, or finding how much of a total was tax.

tax on 100 at 20% // 20
tax off 120 at 20% // 100
tax in 120 at 20% // 20

Recurring schedules: the total of a payment that repeats, such as rent every month for a year and a half.

450 monthly for 18 months // 8,100

Splitting a bill: an amount divided between people, with the odd penny accounted for rather than lost.

split $100 between 3 // $33.33 each, with 1 share paying $33.34
$120 + 18% split 3 ways // $47.20 each

Interest & inflation: compound interest, loan and mortgage repayments, and what an amount of money from one year is worth in another.

interest on 1000 over 3 years at 5% // 157.63
monthly repayment on 200000 over 25 years at 4% // 1,055.67
what is $500 in 1990 worth in 2010 // $834.19

Investments: what a sum grows to at a rate, what a future sum is worth today, and the return on what was invested.

$1,000 after 3 years at 7% // $1,225.04
present value of $1,225.04 after 3 years at 7% // $1,000.00
$500 invested $1,500 returned // 200.00%

Savings goals: how long it takes to reach a target, or how much to put by each month.

how long to save $10,000 at $500 monthly // 20 months
how much per month to save $12,000 in 2 years // $500.00

NPV, IRR & payback: judging an investment from its cash flows, the money paid out first and the money that comes back after: the net present value (NPV, what the flows are worth today) and the internal rate of return (IRR, the rate at which they break even).

npv of -1000, 300, 400, 500 at 10% // -21.04
irr of -1000, 300, 400, 500 // 8.90%

Payroll & take-home: UK take-home pay from a salary, after income tax and National Insurance.

£50,000 after tax // £39,519.60

Comparison shopping: which of two prices is the better deal, and by how much, with vs.

£3 / 500g vs £4 / 750g // the second is cheaper, 11% less

Stocks and crypto: share and coin prices, as in stock(AAPL) and crypto("BTC"), from a data source the host application supplies. A price is live, so there is no fixed answer to show here.

Dates

A line that depends on today is worked out for noon on Wednesday 11 March 2026 in London, the fixed moment these pages are checked against, and the notepad works it out for your own today.

Date literals: a date written day first, year first, or with the month’s name.

25/12/2023 // Monday, December 25, 2023
25 Dec 2026 // Friday, December 25, 2026

Date arithmetic: adding days, weeks, months or hours to a date, or taking them away.

25/12/2023 + 20 days // Sunday, January 14, 2024
30 days from 3 March 2026 // Thursday, April 2, 2026

Relative dates: a day named by its relation to today, such as tomorrow, next friday, three days ago or the end of the month.

tomorrow // Thursday, March 12, 2026, 12:00:00 PM
next friday // Friday, March 13, 2026, 12:00:00 PM
3 days ago // Sunday, March 8, 2026, 12:00:00 PM
end of month // Tuesday, March 31, 2026

Relative months: a month named by its relation to now, which gives the month’s first day.

next month // Wednesday, April 1, 2026

The nth weekday: the nth, or the last, weekday of a month, the way many holidays and meetings are set.

last Friday of November 2026 // Friday, November 27, 2026

Weekdays & week numbers: the day of the week, the month, or the ISO week number a date falls in.

what day is it on 2026-12-25 // Friday
week number of 2026-12-25 // 52

Age: whole years from a birth date, today or on a day you name.

age of 15/06/1990 // 35 years
age of 15/06/1990 on 25/12/2030 // 40 years

Date differences: the span between two dates, or the time until or since one. A count from today includes the part of today already gone, which is why it is not a whole number at noon.

days until 25/12/2026 // 288.50 days
weeks between 01/01/2024 and 01/06/2024 // 21.71 weeks

Timestamps: a Unix timestamp, a count of seconds since 1970, read as the date it names, and a date written as one.

1710000000 as date // Saturday, March 9, 2024, 4:00:00 PM
2024-03-09 as timestamp // 1,709,942,400

Working days: counting only the days that are not weekends (nor public holidays, when the host application supplies them).

25/12/2023 + 5 workdays // Monday, January 1, 2024
working days between 01/01/2024 and 31/01/2024 // 23

Displaying dates: whether a date is spelled out or written in numbers is a setting in the host application, not something a line writes. A date before year 1 is written with its era.

11 March 2026 - 3000 years // Saturday, March 11, 975 BC

Time: clock times, durations, and the span between two times, with frame rates and timecode. A clock time is shown as the time of day, with the days it has moved beside it when it crosses midnight.

9:00am + 3 hours // 12:00:00 PM
11pm + 2 hours // 1:00:00 AM (+1 day)
7:30 to 20:45 // 795 minutes
2h 30m // 150 minutes

Time zones: a time in another place, in several places at once, and the office hours two places share. Without a date the answer is today’s; add on 23 September 2026 to fix the day, since clocks change through the year.

3pm London in Tokyo and New York // Tokyo 12:00 AM (+1 day), New York 11:00 AM
overlap of 9am to 5pm in London and New York // 4 hours: London 1:00 PM to 5:00 PM, New York 9:00 AM to 1:00 PM
3pm London on 23 September 2026 in Tokyo // 11:00 PM

Timesheets: adding up hours worked from clock times or spans, and paying them at an hourly rate.

9am to 5:30pm // 510 minutes
8:15 + 7:45 at £15/hour // £240.00

Units

Unit arithmetic: quantities in different units add and subtract, with the answer in the first one’s unit.

100cm + 2m // 300.00 cm
1 km + 500 m // 1.50 km

Multiplying and dividing units: units multiply, divide and cancel the way numbers do, so an area comes out in square metres and a price per kilogram times a weight comes out in money.

5 m * 3 m // 15.00 m²
3 kg * $5/kg // $15.00

Cooking: oven gas marks, the US, metric and imperial cups, and the number to multiply a recipe by when it has to serve a different number of people.

180C in gas mark // gas 4
1 metric cup in ml // 250.00 ml
scale 4 servings to 6 // 1.50

Converting units: a quantity turned into another unit with to, in or into.

5 km to miles // 3.11 miles
72F to C // 22.22 C

Other representations: as shows a value in another form, such as a percentage or an exact fraction.

0.5 as % // 50.00%
0.75 as fraction // 3/4

Defining your own units: a unit the engine does not ship, named in terms of one it does.

1 sprint = 2 weeks // sprint defined
6 sprints in days // 84 days

CSS units: pixels and rems (a size relative to the page’s base font size) for front-end work, at the usual 16px base or one you name.

16px in rem // 1.00 rem

Screen and image sizes: the shape of a screen or an image (its aspect ratio), the other side after a resize, and how large it prints at a stated density.

1920x1080 as ratio // 16:9
resize 4000x3000 to 1200 wide // 1200 x 900
4000px at 300 dpi // 13.33 in

Rates & speeds: units written with a slash, such as km/h, converted like any other and multiplied or divided back into distance and time.

100 km/h in mph // 62.14 mph
120 km / 60 km/h // 2.00 h

Travel: what a journey burns in fuel, what it costs, and how long it takes.

cost to drive 500 km at 7 l/100km at £1.50/litre // £52.50
250 miles at 60 mph // 4.17 h

Fuel economy: miles per gallon (US or imperial) and litres per 100 km, which run opposite ways (more miles per gallon is fewer litres per 100 km).

40 mpg in l/100km // 5.88 l/100km
35 mpg imperial in l/100km // 8.07 l/100km

Named derived units: quantities multiplied into a named physical unit, such as volts times amps into watts.

230 V * 13 A as W // 2,990.00 W

Electricity: volts, amps, ohms and amp-hours, with Ohm’s law, and the energy a battery holds.

12 V / 2 A // 6.00 Ω
3000 mAh * 3.7 V // 11.10 Wh

Energy units: calories and kilocalories, BTU, therms and electronvolts, beside joules and kilowatt-hours.

2000 kcal in kJ // 8,368.00 kJ
1 therm in kWh // 29.31 kWh

Pressure: pascals, bar, psi, atmospheres and millimetres of mercury, from tyres to blood pressure.

32 psi in bar // 2.21 bar
120 mmHg in kPa // 16.00 kPa

Distances in space: the astronomical unit, the light-year and the parsec.

1 AU in km // 149,597,870.70 km

Moles: the mole and the millimole, chemistry’s count of particles.

1 mol in mmol // 1,000.00 mmol

Surveying & older units: furlongs, chains, rods and other historic units of length and mass.

1 furlong in m // 201.17 m

Geometry: the area, perimeter and volume of the common shapes, from their dimensions.

area of circle radius 5 // 78.54

Health & fitness: body mass index (BMI, a weight measured against a height), and the pace or speed of a run from its distance and time.

bmi(70 kg, 175 cm) // 22.86
pace(10 km, 50 min) // 5:00 /km

Text

Text operations: text in quotes, measured, tested and reshaped: its length, its case, and what it contains.

length of "hello" // 5
"hello world" as upper // HELLO WORLD

Pasted text: the numbers, the amounts of money or one field of JSON pulled out of text pasted from a receipt, a log or an API response.

total of numbers in "Coffee 3.20, lunch 12.50, taxi 18" // 33.70

Text encoding: text turned into base64, a URL-safe form or hex bytes and back again, which is how text travels through systems that accept only certain characters.

"hello" as base64 // aGVsbG8=

Hashing: the digest of a piece of text, a short fingerprint that changes completely when one character changes, used to check that data arrived intact.

sha256("hello") // 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824

Networking: IPv4 and IPv6 subnets, the blocks of addresses a network is divided into: how many machines (hosts) one holds, its netmask, first and last address, and whether an address falls inside it. An IPv6 address is shown in its agreed short form.

hosts in 192.168.1.0/24 // 254
network of 2001:db8:85a3::8a2e:370:7334/64 // 2001:db8:85a3::

Visual

Charts: a series or a function turned into a chart. The engine never draws: it describes the chart as data, and the host application draws it.

plot x^2 from -3 to 3 // x^2 over [-3, 3]

Colours: hex, rgb, hsl and named colours as values, with functions to lighten, mix and check the contrast between them.

lighten(#3366cc, 20%) // #85a3e0
mix(#ff0000, #0000ff) // #800080
contrast(#ffffff, #000000) // 21

Everyday

Coordinates, distance and bearing: places on the globe by latitude and longitude, and the distance and compass direction between two of them.

London = 51.5074°N 0.1278°W // [51.51, -0.13]
Tokyo = 35.6762°N 139.6503°E // [35.68, 139.65]
distance from London to Tokyo // 9,558.57 km

Dice: a random whole number in a range. random seed makes the draws repeat, which is how this one can be checked.

random seed 42
roll(1, 6) // 1

Randomness: random identifiers and choices: a uuid, random hex, a pick from a list, a shuffle and a coin toss, repeatable after a seed.

random seed 42
pick("north", "south", "east", "west") // east
coin // tails

Live data

Weather: the current conditions and temperature for a place, as in weather in London, from a free service that needs no key. The answer is live, so it is named here rather than checked.

Knowledge: a plain-English question, as in ask: distance to the moon, handed to an answering function the host application supplies. The answer comes from that function, so it is named here rather than checked.

Frozen answers: frozen keeps a line’s answer fixed, with the day it was fixed, so a live rate in a shared note reads the same later. It is shown on a plain sum here, since a live rate has no fixed answer to check.

:deposit = 250 * 4 frozen // 1,000
deposit + 50 // 1,050

Working across lines

These forms read other lines of the note, so each is shown as a small note of its own, worked out as one document.

Variables: a name for a value, to use it again later, written with or without a leading colon, and of one word or a few (hourly rate = $50). += and -= keep a running total, and a function of your own is defined the same way.

:a = 10
:b = 20
:a + :b // 30

:budget = 500
budget -= 120 // 380
budget -= 63 // 317

f(x) = 2*x + 1
f(5) // 11

Line references: an earlier line read by its number or its position, and the lines above totalled, by total above or by a line that is only sum or total.

10
20
30
total above // 60
line 1 * 2 // 20

Category tags: a #tag in the middle of a line labels its category and is left out of that line’s own answer. total of, average of and count of gather every line carrying the tag, and total by tag breaks the whole note down. A tag starts with a letter, which keeps it clear of a colour such as #c0ffee.

40 + 15 #grocery      // 55
12 #grocery           // 12
30 #fuel              // 30
total of #grocery     // 67
sum of #grocery       // 67
average of #grocery   // 33.50
count of #grocery     // 2
total by tag          // grocery 67 (69%) · fuel 30 (31%)

Sections: the lines under a markdown heading, down to the next heading at the same level or above, are its section, added up by the heading’s name from anywhere below it.

# Travel
Flights: $450                 // $450.00
Hotel: $220                   // $220.00

# Summary
total of section "Travel"     // $670.00
sum of section "Travel"       // $670.00
average of section "Travel"   // $335.00
count of section "Travel"     // 2

Table columns and table lookups: a markdown table’s column totalled or averaged by its name, and one cell read by the label on its row, the way you read a price off a list.

| item | cost |
| ---- | ---- |
| rent | 1200 |
| food |  300 |
| taxi |   12 |
sum of column "cost" above       // 1,512
average of column "cost" above   // 504
column "cost" for "food"         // 300

Banded rates: a tax, commission or tariff schedule written as a table of bands, where each rate applies only to the part of the amount inside its band.

| from   | rate |
| ------ | ---- |
| 0      | 0%   |
| 10,000 | 20%  |
| 40,000 | 40%  |
45,000 through bands above   // 8,000

Checks: check and a comparison, a line stating something the note should keep true, with a margin written ≈ ... within.

:budget = $1950
:spent = $2010
check :spent <= :budget // ERROR: check failed: $2,010.00 is more than $1,950.00
check 22/7 ≈ pi within 0.1% // ✓ (differs by 0.04%)

Goal seek: working backwards to the input that makes a line reach a target you name.

:deposit = 100000
:rate = 4%
monthly repayment on deposit over 25 years at rate   // 527.84
solve line 3 for deposit = 900                        // 170,507.23

Tracing inputs: which lines fed a result, and which lines fed those.

10
20
total above
line 3 * 2
inputs of line 4   // 60 (line 4) <- 30 (line 3) <- [10 (line 1), 20 (line 2)]

Trigger words: ordinary words such as total and sum are not reserved keywords, so a variable can take one as its name.

:total = 100
:total + 5 // 105

What-if and sweeps: what a line would say if an input were different, without editing the note, or its answers across a range of inputs.

deposit = 100000                                               // 100,000
rate = 4%                                                      // 4.00%
payment = monthly repayment on deposit over 25 years at rate   // 527.84
line 3 with deposit = 150000                                   // 791.76
line 3 for rate from 3% to 5% step 1%                          // [474.21, 527.84, 584.59]