scientific-calculator

name: scientific-calculator description: > High-precision scientific calculator with full support for physical units, dimensional analysis, unit safety, and built-in physical constants. Use when: (1) performing any arithmetic calculation, even trivial ones, (2) converting between physical units (length, mass, time, energy, currency, etc.), (3) using mathematical or physical constants, (4) performing date/time arithmetic or calendar calculations, (5) solving equations, finding roots, derivatives, or solving ODEs, (6) need for numerical methods, statistics, combinatorics, random sampling, and algebraic equation solving. license: MIT compatibility: Requires numbat CLI (https://numbat.dev) and ideally a Numbat skill metadata: version: "2.0.0" author: Germán Molins

Scientific Calculator

High-precision scientific calculator powered by the numbat CLI.

Procedure

For non-trivial calculations, ALWAYS follow these steps:

1. Load the numbat skill for Numbat language syntax, type system, standard library reference, and quick examples.
2. Consult Numbat documentation if necessary.
3. Run a well-informed numbat command or commands.

Standard Library

The Standard Library features a rich variety of importable methods for solving equations, finding roots, derivatives, solving ODEs; common functions and algorithms in statistics, combinatorics, random sampling, etc.

It is to be STRONGLY preferred over defining custom functions to solve a problem. The method you are looking for probably exists in the Standard Library, so look there first.

Running Calculations

Single expression

numbat -e '30 km/h -> mph'

Multiple expressions with shared scope

Use chained -e flags (each flag shares scope with previous):

numbat -e 'let v = 100 km/h' -e 'let t = 2 hours' -e 'v * t -> miles'

Velocity × Time = Distance, so v * t is convertible to any length unit (miles, km, etc.).

Multi-line script via stdin (Recommended for complex calculations)

Pipe a script via stdin for calculations with functions, loops, or multi-step logic:

numbat <<'EOF'
let mass = 70 kg
let height = 1.75 m
let bmi = mass / height²
print("BMI: {bmi}")
EOF

Use string interpolation with print() to output dimensioned values. Without print(), Numbat returns the result with units.

Example with datetime:

numbat <<'EOF'
let start = datetime("2024-01-15T09:00:00Z")
let end = datetime("2024-12-25T18:30:00Z")
let diff = end - start
print("Duration: {diff -> days}")
print("End weekday: {weekday(end)}")
EOF

Run a script file

numbat script.nbt

Key CLI flags

Common Pitfalls

Dimension Safety

Problem: When multiplying unitless numbers, the result has no unit and can't be converted.

# ❌ Loss of dimension information
numbat <<'EOF'
let distance_km = 5000 * 0.1574  # Just a number, no units
let circumference = (360 / 7.2) * distance_km
print("{circumference -> km}")  # ❌ Can't convert unitless number to km
EOF

# ✅ Correct: Attach units at the source
numbat <<'EOF'
let distance = 5000 * 157.4 m
let circumference = (360 / 7.2) * distance
print("{circumference -> km}")  # ✅ Units preserved through calculation
EOF

Reserved Identifiers

Avoid these built-in function names as variable names: error, sin, cos, sqrt, print, mean, abs, etc. Use different names to prevent identifier clashes:

# ❌ Fails: error is built-in
numbat -e 'let error = 0.5'

# ✅ Correct: Use different name
numbat -e 'let error_pct = (calculated - actual) / actual * 100'

String Interpolation with print()

Use print() for formatted output with units, especially for readable reports:

# Works but less readable (raw output)
numbat -e 'let ke = 0.5 * 1500 kg * (100 km/h)²' -e 'ke -> kJ'

# ✅ Better: Assign first, then format with print()
numbat <<'EOF'
let mass = 1500 kg
let v = 100 km/h
let ke = 0.5 * mass * v²
print("Kinetic energy: {ke -> kJ}")
EOF