Math Functions

Advanced mathematical functions and rounding operations.

abs - Absolute Value

Returns the absolute value of a number.

Syntax

{"abs": value}

Parameters

Return Type

Number - Absolute value (always non-negative)

Examples

Basic absolute:

{"abs": -5}                // → 5
{"abs": 10}                // → 10
{"abs": 0}                 // → 0

With variables:

// Data: {"temperature": -15}
{"abs": {"var": "temperature"}}  // → 15

Distance calculation:

{"abs": {"-": [{"var": "x1"}, {"var": "x2"}]}}

max - Maximum Value

Returns the largest value from a list.

Syntax

{"max": [value1, value2, ...]}

Parameters

Return Type

Number - Largest value, or null if empty array

Examples

Basic max:

{"max": [1, 5, 3, 9, 2]}         // → 9
{"max": [-10, -5, -20]}          // → -5

Two values:

{"max": [{"var": "a"}, {"var": "b"}]}

Empty array:

{"max": []}                      // → null

Find highest score:

// Data: {"scores": [85, 92, 78, 95, 88]}
{"reduce": [
  {"var": "scores"},
  {"max": [{"var": "accumulator"}, {"var": "current"}]},
  0
]}

min - Minimum Value

Returns the smallest value from a list.

Syntax

{"min": [value1, value2, ...]}

Parameters

Return Type

Number - Smallest value, or null if empty array

Examples

Basic min:

{"min": [1, 5, 3, 9, 2]}         // → 1
{"min": [-10, -5, -20]}          // → -20

Clamp value:

{"min": [{"var": "input"}, 100]}  // Max value of 100

pow / ** - Power

Raises a number to a power. Alternative to ^ operator.

Syntax

{"pow": [base, exponent]}
{"**": [base, exponent]}

Parameters

Return Type

Number - base^exponent

Examples

Basic power:

{"pow": [2, 3]}                  // → 8
{"pow": [10, 2]}                 // → 100

Square root:

{"pow": [16, 0.5]}               // → 4

Cube:

{"pow": [3, 3]}                  // → 27

round / ROUND - Round Number

Rounds a number to specified decimal places.

Syntax

{"round": [value, decimals]}
{"ROUND": [value]}

Parameters

Return Type

Number - Rounded value

Examples

Round to integer:

{"round": [3.7]}                 // → 4
{"ROUND": [3.2]}                 // → 3
{"round": [3.5]}                 // → 4

Round to decimals:

{"ROUND": [3.14159, 2]}          // → 3.14
{"round": [2.71828, 3]}          // → 2.718

Round to tens:

{"ROUND": [1234, -1]}            // → 1230
{"round": [1567, -2]}            // → 1600

Financial rounding:

{"ROUND": [
  {"*": [{"var": "price"}, {"var": "quantity"}]},
  2
]}

Notes

Uses “round half to even” (banker’s rounding) by default.

roundup / ROUNDUP - Round Up

Always rounds away from zero.

Syntax

{"roundup": [value, decimals]}
{"ROUNDUP": [value, decimals]}

Parameters

Return Type

Number - Rounded up value

Examples

Round up to integer:

{"roundup": [3.1]}               // → 4
{"ROUNDUP": [3.9]}               // → 4
{"roundup": [-3.1]}              // → -4 (away from zero)

Round up to decimals:

{"ROUNDUP": [3.14159, 2]}        // → 3.15
{"roundup": [2.001, 2]}          // → 2.01

Round up to tens:

{"ROUNDUP": [1234, -1]}          // → 1240
{"roundup": [1001, -2]}          // → 1100

Calculate pages:

// Total pages needed
{"ROUNDUP": [
  {"/": [{"var": "items"}, {"var": "perPage"}]},
  0
]}

rounddown / ROUNDDOWN - Round Down

Always rounds toward zero.

Syntax

{"rounddown": [value, decimals]}
{"ROUNDDOWN": [value, decimals]}

Parameters

Return Type

Number - Rounded down value

Examples

Round down to integer:

{"rounddown": [3.9]}             // → 3
{"ROUNDDOWN": [3.1]}             // → 3
{"rounddown": [-3.9]}            // → -3 (toward zero)

Round down to decimals:

{"ROUNDDOWN": [3.14159, 2]}      // → 3.14
{"rounddown": [2.999, 2]}        // → 2.99

ceiling / CEILING - Ceiling

Rounds up to nearest multiple of significance.

Syntax

{"ceiling": [value, significance]}
{"CEILING": [value]}

Parameters

Return Type

Number - Rounded up to nearest multiple

Examples

Round up to integer:

{"ceiling": [4.3]}               // → 5
{"CEILING": [4.1]}               // → 5

Round to specific multiple:

{"CEILING": [4.3, 0.5]}          // → 4.5
{"ceiling": [123, 10]}           // → 130
{"ceiling": [7, 3]}              // → 9 (next multiple of 3)

Price rounding:

{"CEILING": [{"var": "price"}, 0.99]}  // Round to .99

floor / FLOOR - Floor

Rounds down to nearest multiple of significance.

Syntax

{"floor": [value, significance]}
{"FLOOR": [value]}

Parameters

Return Type

Number - Rounded down to nearest multiple

Examples

Round down to integer:

{"floor": [4.9]}                 // → 4
{"FLOOR": [4.1]}                 // → 4

Round to specific multiple:

{"FLOOR": [4.7, 0.5]}            // → 4.5
{"floor": [123, 10]}             // → 120
{"floor": [8, 3]}                // → 6 (previous multiple of 3)

trunc / TRUNC - Truncate

Truncates a number to specified decimal places (removes fractional part).

Syntax

{"trunc": [value, decimals]}
{"TRUNC": [value]}

Parameters

Return Type

Number - Truncated value

Examples

Truncate to integer:

{"trunc": [8.9]}                 // → 8
{"TRUNC": [-8.9]}                // → -8

Truncate to decimals:

{"TRUNC": [8.9876, 2]}           // → 8.98
{"trunc": [-3.789, 1]}           // → -3.7

Truncate to tens:

{"TRUNC": [123.456, -1]}         // → 120

Get integer part:

{"trunc": [{"var": "decimal"}]}  // Remove fractional part

mround / MROUND - Round to Multiple

Rounds to the nearest multiple of a specified value.

Syntax

{"mround": [value, multiple]}
{"MROUND": [value, multiple]}

Parameters

Return Type

Number - Nearest multiple

Examples

Round to nearest multiple:

{"mround": [10, 3]}              // → 9
{"MROUND": [11, 3]}              // → 12
{"mround": [7.5, 2]}             // → 8

Round to nearest 5:

{"MROUND": [13, 5]}              // → 15
{"mround": [12, 5]}              // → 10

Round to decimal multiple:

{"mround": [1.23, 0.1]}          // → 1.2
{"MROUND": [0.567, 0.05]}        // → 0.55

Time rounding (15 minutes):

{"MROUND": [{"var": "minutes"}, 15]}

Complex Examples

Percentage Calculation

{"round": [
  {"*": [
    {"/": [{"var": "part"}, {"var": "total"}]},
    100
  ]},
  1
]}
// Result: percentage with 1 decimal place

Calculate Tax

{"round": [
  {"*": [{"var": "amount"}, {"var": "taxRate"}]},
  2
]}

Clamp Value to Range

{"max": [
  {"min": [{"var": "value"}, {"var": "max"}]},
  {"var": "min"}
]}
// Ensures value is between min and max

Convert to Display Units

{
  "if": [
    {">": [{"var": "bytes"}, 1073741824]},
    {"cat": [
      {"round": [{"/": [{"var": "bytes"}, 1073741824]}, 2]},
      " GB"
    ]},
    {"cat": [
      {"round": [{"/": [{"var": "bytes"}, 1048576]}, 2]},
      " MB"
    ]}
  ]
}

Calculate Compound Interest

{"round": [
  {"*": [
    {"var": "principal"},
    {"-": [
      {"pow": [{"+": [1, {"var": "rate"}]}, {"var": "years"}]},
      1
    ]}
  ]},
  2
]}

Average with Rounding

{"round": [
  {"/": [
    {"sum": [{"var": "values"}]},
    {"length": {"var": "values"}}
  ]},
  2
]}

Price Tier Rounding

{"if": [
  {"<": [{"var": "price"}, 10]},
  {"ceiling": [{"var": "price"}, 0.99]},
  {"ceiling": [{"var": "price"}, 5]}
]}

Best Practices

  1. Always round financial calculations 
    {"round": [amount, 2]}  // 2 decimals for currency
  2. Use appropriate rounding method
    • round - General purpose
    • roundup - Always round up (pages, inventory)
    • rounddown - Always round down (discounts)
    • trunc - Remove decimals without rounding
  3. Round early and often in multi-step calculations 
    {"round": [
  {"+": [
    {"round": [step1, 2]},
    {"round": [step2, 2]}
  ]},
  2
]}
  4. Use ceiling/floor for discretization 
    {"ceiling": [value, binSize]}
  5. Combine min/max for clamping 
    {"max": [minValue, {"min": [value, maxValue]}]}

Excel Compatibility

All operators marked with uppercase names (ROUND, CEILING, etc.) are Excel-compatible:

Performance Notes