List of uncertainty propagation software

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List of uncertainty propagation software used for performing uncertainty propagation calculations:


  • Uncertainty Calculator This is a web interface for uncertainty calculations.
  • Mathos Core Library Uncertainty package Open source (.NET targeting library).
  • Error Propagation Calculator Free cross-platform calculator (OSX/Windows/Linux) written in Python. Essentially a GUI interface for the python Uncertainties library. Very easy to use and install.
  • Das Error Calculator Free/libre cross-platform calculator with minimalistic interface. Designed for use in practical courses at natural sciences. Exposes all formulae needed to calculate the results, interoperability with office, support for physical quantities with units.
  • Dempster Shafer with Intervals (DSI) Toolbox is a MATLAB toolbox for verified computing under Dempster–Shafer theory. It provides aggregation rules, fast (non-)monotonic function propagation, plots of basic probability assignments, verified Fault tree analysis, and much more.
  • EasyGraph is a graphing package that supports error propagation directly into the error bars.
  • Epc is an open source script based tool that calculates the propagation of errors in variables. To quote the text on the Epc web page "This is done by repeated calculation of the expression using variable-values which are generated using a random number generator whose mean and standard-deviation match the values specified for the variable".
  • ErrorCalc is a scientific calculator app for iPhone or iPad that performs error propagation (Supports Algebraic and RPN modes of entry)
  • FuncDesigner
  • GUM Workbench implements a systematic way to analyze an uncertainty problem for single and multiple results. GUM + Monte Carlo. Free restricted educational version available.
  • GUM Tree is a design pattern for propagating measurement uncertainty. There is an implementation in R and add-ons for Excel (real and complex numbers).
  • GUM Tree Calculator is a programmable Windows command-line tool with full support for uncertainty calculations involving real and complex quantities.
  • The Gustavus propagator is an open source calculator that supports error propagation developed by Thomas Huber.
  • Metas.UncLib is a C# software library. There is a wrapper for MATLAB. It supports: multivariate uncertainties, complex values, correlations, vector and matrix algebra.
  • The propagator is a web based tool for propagating errors in data. The tool uses the standard methods for propagation.
  • MUSE Measurement Uncertainty Simulation and Evaluation using the monte carlo method.
  • Uncertainties is a powerful free calculator and Python software library for transparently performing calculations with uncertainties and correlations.
  • SOERP implements second-order error propagation as a free Python library. Calculations are carried out naturally in calculator format and correlations are maintained.
  • Risk Calc supports probability bounds analysis, standard fuzzy arithmetic, and classical interval analysis for conducting distribution-free or nonparametric risk analyses.
  • GUMsim is a Monte Carlo simulator and uncertainty estimator for Windows
  • QMSys GUM is a powerful commercial tool for measurement uncertainty analysis including Monte Carlo simulation for Windows (free restricted educational version available).
  • The Uncertainty Calculator is a Javascript browser-based calculator that performs error propagation calculations.
  • MC-Ed is a native Windows software to perform uncertainty calculations according to the Supplement 1 to the Guide to the expression of uncertainty in measurement using Monte-Carlo method.
  • OpenCOSSAN is a MATLAB toolbox for uncertainty propagation, reliability analysis, model updating, sensitivity and robust design optimization. Allows to interact with 3rd party solvers. Interfaces with HPC through GridEngine and OpenLava.


Name Creator License Programming language Handles correlations? Cross-platform? Calculator? Library? Remarks
Error Propagation Calculator R. Paul Nobrega Free Python Yes Yes Yes No Desktop calculator (Windows/Mac/Linux), handles up to 26 variable and error pairs per computation. Evaluates native python expressions. No prior knowledge of python language is required for use. Windows installer includes python dependencies.
Abacus Mischa Megens Free C, Win32 Yes No Yes No Desktop calculator (Windows), handles multiple expressions
App::ErrorCalculator Steffen Müller GNU GPL Perl No Yes Library and script to process tabular values
Colby College Uncertainty Calculator T. W. Shattuck Unknown JavaScript Yes Yes Yes No Web browser based. Formula input, then asks for values of variables.
Das Error Calculator Gregor Bollerhey GNU GPL Python Yes Yes Yes Standalone notebook calculator, optimized for lab classes (displays formula, export to spreadsheet or latex). Supports physical quantities with units.
Dempster Shafer with Intervals (DSI) Toolbox Gabor Rebner Free for private and academic use MATLAB No Yes Verified computation of basic probability assignments and Fault tree analysis under Dempster–Shafer theory. Fast evaluation of (non-) monotonic system functions and aggregation rules.
Experimental Data Analyst (EDA) David Harrison Proprietary Mathematica Yes No Yes Library
EPC: error-propagating calculator Dan Kelley GNU GPL Perl Yes Yes Yes Perl Script. Monte Carlo evaluation of an expression.
ErrorCalc iPhone/iPad calculator app Thomas Huber Proprietary Unknown No No Yes No Scientific calculator app for iPhone or iPad that performs error propagation (Algebraic and RPN Entry modes)
FuncDesigner Dmitrey BSD Python No Yes Yes Library and stand-alone (via the Python shell). Involves Automatic differentiation (possibly large-scale sparse)
GUM Workbench Metrodata GmbH Proprietary Delphi Yes Yes No Standalone. Detailed consequences of a model equation. GUM + Monte Carlo. Free restricted educational version available.
GUM_MC Jean-Marie Biansan GNU GPL Lazarus Yes Yes Yes No Standalone. Gum framework and Monte Carlo method.
fussy S. Bhatnagar Free but copyrighted C Yes No Yes Yes Scripting language called 'fussy', similar to C.
Gustavus Adolphus error propagation calculator Thomas Huber GNU GPL Unknown No No Yes No Executable only. Desk calculator style (with no expression parentheses). error propagation calculator Richard Laffers Creative Commons JavaScript No Yes Yes No Web browser based. Desk calculator style.
Measurement Software Toolkit Industrial Research Ltd Free for non-commercial use R; Excel plug-in Yes Yes Yes Library and plug-in
GUM Tree Calculator (GTC) Industrial Research Ltd Single-user, non-transferable. Free. Python Yes No Yes No A programmable command-line calculator for Windows. Suitable for calculations involving real and complex quantities. Programmable in Python. An IDE with syntax highlighting and on-line help is included.
MUSE Measurement Uncertainty Research Group, ETH Zürich Free for non-commercial use C++ Yes Yes No Standalone. Monte-Carlo sampling. Interprets an XML model description file.
Metas.UncLib Michael Wollensack, METAS Free use; redistribution prohibited C#; MATLAB wrapper Yes No Yes Yes Library, and command-line calculator (through Matlab)
Number::WithError Steffen Müller GNU GPL Perl No No Yes Library
uncertainties Eric O. Lebigot (EOL) BSD Python Yes Yes Yes Yes Library and stand-alone command-line calculator (via the Python shell). Fully transparent calculations with correlations. Also handles matrices with uncertainties. Automatically calculates all the derivatives of an expression
soerp Abraham Lee BSD Python Yes Yes Yes Yes Free Python library and command-line calculator. Fully transparent second-order calculations with correlations. Automatically calculates all the first and second derivatives of an expression using the free Python package ad
Risk Calc Scott Ferson Proprietary C++ Yes Yes Probabilistic and interval uncertainty. Also handles uncertainty about correlations.
S&T Missouri Uncertainty Calculator Gary L. Bertrand Unknown JavaScript No Yes Yes No Web browser based. Desk calculator style.
Uncertainty Calculator; Wilfrid Laurier University Terry Sturtevant Unknown JavaScript No Yes Yes No Web browser based. Desk calculator style.
propagate Andrej-Nikolai Spiess GNU GPL R Yes Yes No Yes An R package that conducts error propagation by first- and second-order Taylor approximation (GUM 2008) and Monte-Carlo simulation (GUM 2008 S1), using full covariance structure.
GUMsim QuoData GmbH Proprietary Delphi Yes No Yes No Standalone. Detailed consequences of a model equation.
QMSys GUM Qualisyst Ltd. Proprietary Unknown Yes No Standalone. Linear/nonlinear models, Monte Carlo method. (free restricted educational version available)
MC-Ed Florian Platel (MetGen) Free Embarcadero Delphi No No Yes No Desktop calculator (Win32 native application). Monte-Carlo simulations.
OpenCOSSAN Institute of Risk and Uncertainty, University of Liverpool GNU GPL MATLAB Yes Yes No Yes Provides an object-oriented programming interface to advanced algorithms and solution sequences.

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