calculate

Evaluate mathematical expressions numerically using SymPy.

This tool is intended for reliable arithmetic and formula evaluation. It returns floating-point numeric results (not symbolic expressions).

Action Format

{"type": "calculate", "value": "2 * 20 * sin(30 * pi / 180) / 9.8", "out": "$result"}

Parameters

Expression Syntax

Arithmetic

• +, -, *, /
• ** (power)
• % (modulo)

Constants

• pi
• E (Euler’s number)

Trigonometry (radians only)

• sin(x), cos(x), tan(x)
• asin(x), acos(x), atan(x)

⚠ Important: All trigonometric functions expect radians.
Degrees must be converted explicitly, e.g. sin(30 * pi / 180).

Other functions

• sqrt(x)
• log(x) (natural log)
• ln(x) (alias for natural log)
• exp(x)
• abs(x)
• factorial(n)

Variable Substitution

Use variables to substitute numeric values into expressions.

{
  "type": "calculate",
  "value": "2 * v * sin(theta * pi / 180) / g",
  "variables": {"v": 20, "theta": 30, "g": 9.8},
  "out": "$time"
}

All variables must resolve to numeric values after substitution. If unresolved symbols remain, evaluation may fail.

Equation Solving (Advanced)

This tool supports simple equation solving via SymPy.

Using =

Expressions containing a single = are interpreted as equations.

{"type":"calculate","value":"x**2 - 4 = 0","out":"$roots"}

Using solve(...)

You may explicitly call solve:

{"type":"calculate","value":"solve(x**2 - 4, x)","out":"$roots"}

Output format for solutions

• Multiple solutions are returned as a comma-separated string
• Each solution is numerically evaluated to the requested precision

Example result:

-2.000000000, 2.000000000

If individual values are needed, use downstream tools (e.g. split).

Output

• The result is returned as a string representation of a numeric value
• Floating-point evaluation is always used
• Integer expressions will still return floats (e.g. 14.000000000)

To convert to an integer, use a coercion tool such as:

{"type":"coerce","value":"$result","coercion":"to-int","out":"$int_result"}

The Skills runtime binds the returned value to the variable specified by out.

Failure Conditions

The tool may fail if:

• The expression is syntactically invalid
• Variables are missing or non-numeric
• Symbols remain unresolved after substitution
• The expression cannot be numerically evaluated

In these cases, the tool returns a failure status rather than a value.

When to Use

• Reliable arithmetic and formula evaluation
• Physics and engineering calculations
• Numeric evaluation where LLM arithmetic is unreliable

Avoid using this tool for:

• Symbolic manipulation
• Algebraic simplification
• Proofs or exact symbolic results