Uncertainty Calculator

"Help you get rid of the Physical Chemistry Experiment course in CCME at PKU!"

A Python tool for automated error propagation in physical experiments. This calculator uses symbolic differentiation to compute partial derivatives and propagate uncertainties, generating detailed LaTeX output for your reports.

📑 Table of Contents

• ✨ Features
• 🚀 Installation
• 📖 Usage
  • Code layout
  • 1. Define the Equation
  • 2. Define Variables
  • 3. Configuration
  • 4. Run the Calculator
  • 5. Render the LaTeX String
• 📊 Output Example
• 🙌 Acknowledgements
• 📄 License

✨ Features

• Symbolic Differentiation: Automatically calculates partial derivatives using sympy.
• Automated Error Propagation: Computes the final uncertainty based on the standard error propagation formula.
• LaTeX Output: Generates ready-to-use LaTeX code for equations, derivatives, and substitution steps.
• Customizable: Configurable decimal precision, units, and output formatting.

🚀 Installation

Requirements

• Python: 3.12+
• Dependencies: sympy

Install via uv

We recommend using uv for fast environment management:

uv venv --python 3.12
source .venv/bin/activate
uv pip install -e .[dev]

📖 Usage

The calculator is designed to be used as a Python module. Below is a complete example of how to configure and run calculation.

Code layout

The core logic is organized by responsibility:

• calculator.py: orchestrates the pipeline
• parsers.py: builds symbols/mappings from inputs
• compute.py: performs derivatives and numeric propagation
• render.py: produces LaTeX output
• _types.py: input dataclasses and type aliases
• format.py / validation.py: shared helpers

1. Define the Equation

The equation can be defined using the Equation class. latex_name is the rendered result symbol, while expression is the internal symbolic formula written with variable names.

from uncertainty_calculator import Equation

# Define equation
equation = Equation(
    latex_name=r"\zeta",
    expression=r"(K*pi*eta*u*l)/(4*pi*phi*e_0*e_r)",
)

2. Define Variables

Variables can be defined using the Variable class for structured input.

from uncertainty_calculator import Variable

# Define variables
variables = [
    Variable(name="K", value=4.0, uncertainty=0.0, latex_name="K"),
    Variable(name="eta", value=0.9358e-3, uncertainty=5.773502691896258e-05, latex_name=r"\eta"),
    Variable(name="u", value=3.68e-5, uncertainty=0.11e-5, latex_name="u"),
    Variable(name="l", value=0.2256, uncertainty=0.0019, latex_name="l"),
    Variable(name="phi", value=100.0, uncertainty=0.5773502691896257, latex_name=r"\varphi"),
    Variable(name="e_0", value=8.8541878128e-12, uncertainty=0.0, latex_name=r"\varepsilon_0"),
    Variable(
        name="e_r", value=78.7, uncertainty=0.057735026918962574, latex_name=r"\varepsilon_\text{r}"
    ),
]

3. Configuration

Configure the output format, precision, and units.

from uncertainty_calculator import Digits

# Set digits of results
digits = Digits(mu=3, sigma=3)

# Set units of results
last_unit = r"\text{V}"  # Use None if dimensionless
# last_unit = None

# Print separately or integrally
separate = False

# Insert numbers or not
insert = False

# Include equation number or not
include_equation_number = True

4. Run the Calculator

Import the UncertaintyCalculator and execute the calculation.

from uncertainty_calculator import UncertaintyCalculator

calculator = UncertaintyCalculator(
    digits=digits,
    last_unit=last_unit,
    separate=separate,
    insert=insert,
    include_equation_number=include_equation_number,
)

latex_string = calculator.run(equation=equation, variables=variables)

print(latex_string)

5. Render the LaTeX String

from IPython.display import Latex

Latex(latex_string)

📊 Output Example

The tool generates LaTeX code that renders to standard physical chemistry calculation steps:

\begin{equation}
\begin{aligned}
\zeta&=\frac{K \eta l u}{4 \varepsilon_0 \varepsilon_\text{r} \varphi}=0.111\ \text{V}\\
\\
\frac{\partial \zeta }{\partial \eta }&=\frac{K l u}{4 \varepsilon_0 \varepsilon_\text{r} \varphi}=1.2 \times 10^{2}\\
\frac{\partial \zeta }{\partial u }&=\frac{K \eta l}{4 \varepsilon_0 \varepsilon_\text{r} \varphi}=3.0 \times 10^{3}\\
\frac{\partial \zeta }{\partial l }&=\frac{K \eta u}{4 \varepsilon_0 \varepsilon_\text{r} \varphi}=0.49\\
\frac{\partial \zeta }{\partial \varphi }&=- \frac{K \eta l u}{4 \varepsilon_0 \varepsilon_\text{r} \varphi^{2}}=-0.0011\\
\frac{\partial \zeta }{\partial \varepsilon_\text{r} }&=- \frac{K \eta l u}{4 \varepsilon_0 \varepsilon_\text{r}^{2} \varphi}=-0.0014\\
\\
\sigma_{\zeta}&=\sqrt{\left(\frac{\partial \zeta }{\partial \eta } \sigma_{\eta}\right)^2+\left(\frac{\partial \zeta }{\partial u } \sigma_{u}\right)^2+\left(\frac{\partial \zeta }{\partial l } \sigma_{l}\right)^2+\left(\frac{\partial \zeta }{\partial \varphi } \sigma_{\varphi}\right)^2+\left(\frac{\partial \zeta }{\partial \varepsilon_\text{r} } \sigma_{\varepsilon_\text{r}}\right)^2}\\
&=\sqrt{\left(0.0069\right)^2+\left(0.0033\right)^2+\left(0.00094\right)^2+\left(-0.00064\right)^2+\left(-8.2 \times 10^{-5}\right)^2}\\
&=0.00773\ \text{V}\\
\\
\zeta&=\left (0.111 \pm 0.00773 \right )\ \text{V}
\end{aligned}
\end{equation}

Rendered results:

🙌 Acknowledgements

• SymPy: https://github.com/sympy/sympy
• LaTeX Live: https://latexlive.com

📄 License

This project is licensed under the MIT License.