PanPhyPlot · Formula guide

A little math for your data

Find the syntax you need for a formula column, from a simple square to the mean of repeat readings.

Working on a fit? See custom fit syntax.

Start here

Write your first formula

Choose Data → Formula in the app’s toolbar.
Use a column letter, such as B^2, or a unique column name, such as T^2. No leading = is needed.
Check the result preview, give the new column a name and unit, then choose Apply.

Reading the examples

A and B below mean column A and column B in the same row. Replace them with the letters or names in your own sheet. Formula columns update when the source data changes.

Build an expression

Operators

Write multiplication explicitly with *, and use parentheses to control the order of calculation.

Arithmetic operators and examples
Operator	Meaning	Example
`+`	Add	`A + B`
`-`	Subtract / negative sign	`A - B`, `-A`
`*`	Multiply	`2*A`
`/`	Divide	`B/A`
`^`	Power	`A^2`, `B^0.5`
`%`	Remainder (mod)	`A % 2`
`( )`	Group parts of an expression	`(A + B)/2`

Transform a reading

Functions

Put the input inside parentheses: sqrt(B) takes the square root of each value in column B.

Trigonometry

Angles are in radians. For degrees, convert first: sin(A*pi/180).

Trigonometric functions
Function	Meaning	Example
`sin(A)`	Sine	`sin(A)`
`cos(A)`	Cosine	`cos(A)`
`tan(A)`	Tangent	`tan(A)`
`asin(A)`, `acos(A)`, `atan(A)`	Inverse trig	`atan(B/A)`

Powers, roots and absolute value

Roots and absolute value
Function	Meaning	Example
`sqrt(A)`	Square root	`sqrt(A)`
`cbrt(A)`	Cube root	`cbrt(B)`
`abs(A)`	Absolute value	`abs(B)`

Logs and exponentials

Logarithms need a positive input. A real square root needs a non-negative input.

Logarithms and exponentials
Function	Meaning	Example
`log(A)`	Natural log (base `e`)	`log(B)`
`log10(A)`	Base-10 log	`log10(B)`
`exp(A)`	`e^A`	`exp(A)`

Rounding

Rounding functions
Function	Meaning	Example
`round(A)`	Round to nearest integer	`round(3.6)` gives `4`
`floor(A)`	Round down	`floor(3.9)` gives `3`
`ceil(A)`	Round up	`ceil(3.1)` gives `4`

Repeat readings

Functions for readings in the same row
Function	Meaning	Example
`mean`	Arithmetic mean	`mean(B, C, D)`
`median`	Middle reading	`median(B, C, D)`
`min`, `max`	Smallest or largest reading	`max(B, C, D)`
`halfspread`	Half the range (at least two readings)	`halfspread(B, C, D)`

These five functions leave out blank readings among their inputs. Other expressions stay blank when a required input is missing or invalid.

Values you can use

Constants

Mathematical constants
Constant	Value (approx.)	Example
`pi`	3.14159...	`2piA`
`e`	2.71828...	`e^A` or `exp(A)`
`tau`	6.28318... (`2*pi`)	`tau*A`

Case matters

Use lowercase pi and e. Column letters take priority: E refers to column E when it exists, so use e or exp(A) for Euler’s number.

Try it on your sheet

Formula ideas

Use these expressions in Data → Formula, replacing the column letters as needed.

Reciprocal: 1/AA must not be zero.
Square: A^2Useful for a period-squared graph.
Square root: sqrt(B)Use non-negative values.
Natural log: log(B)Use positive values.
Mean of repeats: mean(B, C, D)Combine readings from the same row.
Magnitude: abs(B)Remove the sign of a reading.
Sine wave: sin(2*pi*A)One cycle per unit of A.
Average two columns: (A+B)/2Both readings must be present.

In the fit inspector

Custom fit syntax

A custom fit uses x for the independent variable and parameter names such as a and b. For a straight line, enter a*x+b. The operators, trig, roots, logs and rounding syntax above work here too.

See fit types and custom formulas in the manual →

Formula not working?

Check spelling and capitalization, column names and parentheses. Use * for multiplication. A formula column needs a finite real result; division by zero or an out-of-range input leaves the result blank.

A quick reference to the Math.js syntax used by PanPhyPlot.