EDUCATION DECISION WORKBENCH
Propagate independent standard uncertainties through additive or multiplicative measurement models with every contribution disclosed.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous, policy-approved information. Results remain in this browser tab until you copy or download them.
Transparent method
For z = Σ(cᵢxᵢ), standard uncertainty u(z) = √Σ(cᵢuᵢ)². For z = Πxᵢ^pᵢ, relative uncertainty u(z)/|z| = √Σ[pᵢu(xᵢ)/|xᵢ|]², and absolute uncertainty is |z| times that relative value. These first-order root-sum-square rules assume independent standard uncertainties and sufficiently small variations around the entered values. The absolute uncertainty uses the same unit as the calculated result, while the relative percentage makes contributions comparable. A large percentage is a prompt to inspect instrument choice, repeated measurements, model sensitivity, and whether linear propagation is adequate. Round the uncertainty and reported value together according to the laboratory convention instead of copying every displayed digit.
Confirm the question, variables, units, source data, measurement precision, and the model expected by the current course or laboratory. Keep an untouched copy of observations before excluding or transforming any value.
Run the worked example first, inspect every intermediate row, compare units and signs, and look for a result that conflicts with the graph, physical system, chemical equation, or learning objective.
Record the method, assumptions, units, rounding, data limitations, and any excluded observations. Compare the exported report with an independent calculation or approved reference before assessment or laboratory use.
How to interpret the result
Use this workbench after measuring inputs for a derived quantity such as density, speed, area, resistance, or a difference between readings. It supports laboratory reports that require a value with an uncertainty budget and helps learners see which measurement contributes most. Use a different method when inputs are correlated, uncertainties are asymmetric, or the model is strongly nonlinear over the uncertainty range.
The density example models mass divided by length, width, and height. Mass has power +1 and all three dimensions have power −1. The workbench calculates the nominal density, converts each absolute uncertainty to a relative contribution multiplied by its power, combines those contributions by root sum of squares, and converts the combined relative uncertainty back to an absolute uncertainty beside the result.
For z = Σ(cᵢxᵢ), standard uncertainty u(z) = √Σ(cᵢuᵢ)². For z = Πxᵢ^pᵢ, relative uncertainty u(z)/|z| = √Σ[pᵢu(xᵢ)/|xᵢ|]², and absolute uncertainty is |z| times that relative value. These first-order root-sum-square rules assume independent standard uncertainties and sufficiently small variations around the entered values.
The absolute uncertainty uses the same unit as the calculated result, while the relative percentage makes contributions comparable. A large percentage is a prompt to inspect instrument choice, repeated measurements, model sensitivity, and whether linear propagation is adequate. Round the uncertainty and reported value together according to the laboratory convention instead of copying every displayed digit.
Do not enter tolerance as standard uncertainty without the required conversion, add independent uncertainties linearly when the required method is root sum of squares, ignore covariance from shared instruments, use percent values in an absolute-uncertainty column, or confuse a confidence interval with a standard uncertainty. Preserve units and significant figures and state the uncertainty model in the report.
Learning boundary
This browser-local workbench calculates only from the entered model and observations. It cannot validate an experiment, balance an equation, establish causation, certify laboratory safety, diagnose learning, or replace the method required by a teacher, curriculum, laboratory, or institution.
Review checklist
Practical questions
No. The calculation runs in the current browser tab. Avoid personal information and retain laboratory data in the system authorized by the school.
Treat it as an editable analysis aid. Show your own reasoning, cite the required sources, follow academic-integrity rules, and use the method requested by your course.
No. Check dimensions, graph shape, assumptions, measurement uncertainty, significant figures, and whether another model explains the observations better.
YOUR NIRMION
