Math functions you can use in calculator formulas

Calconic formulas can do much more than add and multiply fields. With math functions you can round results, set a minimum or maximum value, raise numbers to a power, calculate square roots, work out averages and much more. This article lists all the main functions, with simple and real-world examples for each one.

Every input field in your calculator has its own unique ID, such as #1, #2 or #3. You use these IDs inside formulas, for example #1 + #2. If you are new to formulas, start with Writing a formula for a custom calculator widget.

For each function below you will find a short explanation, simple examples you can copy and adjust right away, and real-world examples – complete formulas for common calculator types.

How functions work

A function is a name followed by brackets. Whatever you put inside the brackets is what the function works on:

function(value)
function(value1, value2, ...)

The value can be a plain number, a field ID, or a whole formula:

round(4.7)              → 5
round(#1)               → rounds the value of field #1
round(#1 * #2 / 3)      → rounds the result of the whole calculation

You can also put functions inside other functions:

round(max(#1, #2) * 1.21, 2)

Basic operators

Before getting to functions, here are the operators you can use between values:

Calculations follow the standard order: brackets first, then powers, then multiplication and division, then addition and subtraction. When in doubt, add brackets.

Rounding functions

Rounding is the most common need in calculators – prices, quantities and measurements rarely look good with ten decimal places.

round() – round to the nearest number

Rounds to the nearest whole number. Halves (.5) are rounded up. Add a second value to choose how many decimal places to keep: round(value, decimals).

Simple examples

Real-world examples

Price with 21% VAT, rounded to cents (#1 = price without VAT):

round(#1 * 1.21, 2)

BMI with one decimal (#1 = weight in kg, #2 = height in cm):

round(#1 / (#2 / 100) ^ 2, 1)

70 kg and 175 cm gives 22.9.

Percentage, rounded to a whole number (#1 = part, #2 = total):

round(#1 / #2 * 100)

45 out of 60 gives 75.

ceil() – always round up

Rounds up to the next whole number, even if the decimal part is tiny. Whole numbers stay as they are.

Simple examples

Real-world examples

Paint cans needed (#1 = wall area in m², one can covers 10 m²):

ceil(#1 / 10)

A 43 m² wall gives 5 cans.

Tile boxes needed with 10% extra for cutting (#1 = floor area in m², #2 = m² per box):

ceil(#1 * 1.1 / #2)

20 m² with boxes of 1.44 m² gives 16 boxes.

Billable hours, where every started hour counts (#1 = minutes worked):

ceil(#1 / 60)

95 minutes gives 2 hours.

Number of buses needed for a group (#1 = people, 50 seats per bus):

ceil(#1 / 50)

More details in Rounding calculator results up to the next integer.

floor() – always round down

Rounds down to the previous whole number.

Simple examples

Real-world examples

How many items the customer can afford (#1 = budget, #2 = price per item):

floor(#1 / #2)

A budget of 100 and items costing 30 gives 3 items.

Full boxes that can be packed (#1 = number of items, 12 per box):

floor(#1 / 12)

Age in full years (#1 = age in months):

floor(#1 / 12)

More details in Rounding calculator results down to the nearest integer.

fix() – remove the decimal part

Cuts off the decimals and keeps only the whole number part. For positive numbers it works like floor(); for negative numbers it rounds toward zero.

Simple examples

For comparison, floor(-4.9) gives -5.

Use it for: results that can be negative (profit/loss, temperature differences) where you just want to drop the decimals.

Rounding to the nearest 5, 10, 100…

There is no separate function for this, but you can combine rounding with division and multiplication: divide by the step, round, then multiply back.

Minimum and maximum values

max() – the highest value (set a minimum)

Returns the largest of the values you give it. You can pass two or more values.

The most common use is to make sure a result never goes below a certain number: max(#1, 3) means "use #1, but at least 3".

Simple examples

Note: max(#1, 3) gives the same result as the conditional formula ((#1 < 3)?(3):(#1)), but is shorter and easier to read.

Real-world examples

Shipping costs 2 per kg, but at least 15 (#1 = weight in kg):

max(#1 * 2, 15)

Minimum order quantity of 10 (#1 = quantity entered, #2 = price per item):

max(#1, 10) * #2

A customer ordering 3 items at 5 each still pays for 10: 50.

Minimum one billable hour (#1 = hours, #2 = hourly rate):

max(#1, 1) * #2

Remaining balance that can't go negative (#1 = budget, #2 = spent):

max(#1 - #2, 0)

min() – the lowest value (set a maximum)

Returns the smallest of the values you give it.

The most common use is to make sure a result never goes above a certain number: min(#1, 100) means "use #1, but no more than 100".

Simple examples

Note: min(#1, 100) gives the same result as ((#1 > 100)?(100):(#1)).

Real-world examples

10% discount, but no more than 50 (#1 = order total):

min(#1 * 0.10, 50)

Quantity limited to available stock (#1 = quantity ordered, #2 = in stock):

min(#1, #2)

Insurance payout limited to 5 000 (#1 = damage amount):

min(#1, 5000)

Which one should I use?

It's easy to mix them up, so here is a simple rule:

Keeping a result between a minimum and a maximum

Put max() inside min():

Real-world example – a 5% fee, but never less than 10 and never more than 200 (#1 = amount):

min(max(#1 * 0.05, 10), 200)

Positive and negative values

abs() – absolute value

Removes the minus sign, so the result is always positive.

Simple examples

Real-world examples

Difference between planned and actual cost, whichever is higher (#1 = planned, #2 = actual):

abs(#1 - #2)

Percentage difference (#1 = old value, #2 = new value):

round(abs(#1 - #2) / #1 * 100, 1)

From 200 to 170 gives 15 (%).

sign() – positive, negative or zero

Returns 1 for positive numbers, -1 for negative numbers and 0 for zero.

Simple examples

Real-world example – add a one-time setup fee of 25 only if something is ordered (#1 = quantity, price 10 each):

#1 * 10 + 25 * sign(#1)

Quantity 0 gives 0; quantity 3 gives 55.

Powers and roots

pow() – raise to a power

pow(x, y) multiplies x by itself y times. It does exactly the same as x ^ y, so you can use whichever you find easier to read.

Simple examples

Real-world examples

Area of a square room (#1 = side length):

#1 ^ 2

Compound interest (#1 = amount, #2 = yearly rate in %, #3 = years):

round(#1 * pow(1 + #2 / 100, #3), 2)

10 000 at 5% for 10 years gives 16 288.95.

Monthly loan payment (#1 = loan amount, #2 = yearly interest rate in %, #3 = number of months):

round((#1 * (#2 / 100 / 12)) / (1 - pow(1 + #2 / 100 / 12, -#3)), 2)

A 20 000 loan at 6% for 60 months gives 386.66 per month.

Note: this loan formula divides by zero if the interest rate is 0. If 0% is possible in your calculator, wrap it in an IF condition: ((#2 == 0)?(round(#1 / #3, 2)):(...loan formula...)). See conditional formulas.

sqrt() – square root

Simple examples

Real-world examples

Side length of a square from its area (#1 = area in m²):

sqrt(#1)

Diagonal of a screen, room or rectangle (#1 = width, #2 = height):

round(sqrt(#1 ^ 2 + #2 ^ 2), 1)

120 × 70 gives 138.9.

cbrt() – cube root

Simple examples

Real-world example – edge length in metres of a cube-shaped tank (#1 = volume in litres):

round(cbrt(#1 / 1000), 2)

1 000 litres gives 1 m.

nthRoot() – any root

nthRoot(x, n) returns the n-th root of x. Note the capital R.

Simple examples

Real-world example – average yearly growth rate (CAGR) in % (#1 = start value, #2 = end value, #3 = years):

round((nthRoot(#2 / #1, #3) - 1) * 100, 2)

Growing from 100 to 200 in 5 years gives 14.87 (%).

hypot() – length of the diagonal

hypot(a, b) is a shortcut for sqrt(a^2 + b^2). It also works with three values for the diagonal of a box.

Simple examples

Real-world example – rafter length of a roof (#1 = horizontal run, #2 = rise):

round(hypot(#1, #2), 2)

Division and remainders

mod() – remainder after division

mod(x, y) returns what is left over after dividing x by y.

Simple examples

Real-world examples

Full boxes and loose items (#1 = number of items, 12 per box) – use two formula fields:

floor(#1 / 12)    → full boxes
mod(#1, 12)       → items left over

30 items gives 2 full boxes and 6 loose items.

Hours and minutes from total minutes (#1 = minutes):

floor(#1 / 60)    → hours
mod(#1, 60)       → minutes

135 minutes gives 2 hours and 15 minutes.

Weeks and days (#1 = number of days):

floor(#1 / 7)     → weeks
mod(#1, 7)        → days

Extra charge for odd quantities (for example, items sold in pairs):

((mod(#1, 2) == 1)?(5):(0))

Totals and averages

These functions accept as many values as you need, separated by commas.

sum() – total

Simple examples

sum(#1, #2, #3) works the same as #1 + #2 + #3, but is easier to read when you have many fields.

mean() – average

Simple examples

Real-world example – average score from several rating fields:

round(mean(#1, #2, #3, #4), 1)

median() – middle value

Sorts the values and returns the one in the middle. Unlike the average, one very high or very low value does not pull it up or down.

Simple examples

prod() – multiply all values

Simple examples

Real-world example – concrete needed in m³ (#1 = length, #2 = width, #3 = thickness in cm):

round(prod(#1, #2, #3 / 100), 2)

Logarithms and exponents

These are mostly used for finance, science and engineering calculators.

exp() – e to the power of x

Simple examples

Real-world examples

Continuously compounded interest (#1 = amount, #2 = rate in %, #3 = years):

round(#1 * exp(#2 / 100 * #3), 2)

Value after depreciation or decay (#1 = starting value, #2 = decay rate in %, #3 = years):

round(#1 * exp(-#2 / 100 * #3), 2)

log() – logarithm

log(x) returns the natural logarithm (base e). Add a second value to choose a different base: log(x, base).

Simple examples

Real-world examples

Years until an investment doubles (#1 = yearly rate in %):

round(log(2) / log(1 + #1 / 100), 1)

At 7% the money doubles in about 10.2 years.

Full years needed to reach a savings goal (#1 = current amount, #2 = goal, #3 = yearly rate in %):

ceil(log(#2 / #1) / log(1 + #3 / 100))

From 1 000 to 2 000 at 7% gives 11 years.

log10() and log2()

Shortcuts for base-10 and base-2 logarithms.

Real-world example – power ratio in decibels (#1 = output power, #2 = input power):

round(10 * log10(#1 / #2), 1)

A ratio of 100 gives 20 dB.

Trigonometry

Calconic supports sin(), cos(), tan() and their inverses asin(), acos(), atan().

Important: these functions work in radians, not degrees.

• To use an angle in degrees, multiply it by pi / 180 inside the function.
• To get a result in degrees from asin(), acos() or atan(), multiply the result by 180 / pi.

Simple examples

Tip: wrap trigonometry results in round() – otherwise you may see results like 0.49999999999999994 instead of 0.5.

Real-world examples

Height of a ramp (#1 = ramp length, #2 = angle in degrees):

round(#1 * sin(#2 * pi / 180), 2)

Roof pitch angle in degrees (#1 = rise, #2 = run):

round(atan(#1 / #2) * 180 / pi, 1)

Slope in % converted to degrees (#1 = slope in %):

round(atan(#1 / 100) * 180 / pi, 1)

A 10% slope gives 5.7°.

Combinations and factorials

factorial() – n!

Multiplies all whole numbers from 1 up to n. You can also write n!.

Real-world example – number of ways to seat #1 guests in a row: factorial(#1).

combinations() – how many ways to choose

combinations(n, k) – how many different groups of k items can be picked from n items when order does not matter.

Real-world examples

Possible pizzas with 3 toppings out of #1 available:

combinations(#1, 3)

Number of matches in a round-robin tournament (#1 = teams):

combinations(#1, 2)

8 teams play 28 matches.

permutations() – how many ways to arrange

Same as above, but order matters.

Real-world example – ways to award gold, silver and bronze among #1 participants: permutations(#1, 3).

Constants

You can use these named values directly in a formula:

Simple examples

Real-world examples

Area of a circle from its diameter (#1 = diameter):

round(pi * (#1 / 2) ^ 2, 2)

Volume of a round pool in litres (#1 = diameter in m, #2 = depth in m):

round(pi * (#1 / 2) ^ 2 * #2 * 1000)

A 4 m pool, 1.2 m deep, holds 15 080 litres.

Combining functions with IF conditions

All functions can be used inside conditional formulas, and conditions can be used inside functions. The IF syntax is:

((condition)?(value if true):(value if false))

Simple examples

Real-world example – free shipping over 100, otherwise 5% of the order but at least 4.99 (#1 = order total):

((#1 >= 100)?(0):(max(round(#1 * 0.05, 2), 4.99)))

Read more in Writing a conditional formula (IF) for a calculator widget.

Quick reference

Tips

• Function names are case-sensitive. Write round(), not Round() or ROUND(). Note nthRoot() has a capital R.
• Use commas between values inside a function: max(#1, #2). Use a dot for decimals: 0.25, not 0,25.
• Check your brackets. Every opening bracket needs a closing one. Long formulas are easier to check if you build them step by step.
• Round at the end. Rounding in the middle of a formula can make the final result less accurate. Wrap the whole formula instead: round(#1 #2 1.21, 2).
• Avoid dividing by zero. If a field can be empty or 0, protect divisions with an IF condition or max(#2, 1).
• Test with real numbers. Use the preview to try a few typical values and edge cases (0, very large numbers, negative numbers) before publishing.