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Measurement Uncertainty Calculator
Tools / Chemistry / Measurement Uncertainty Calculator

Measurement Uncertainty Calculator (Concentration from Weighing and Volume)

Calculate uncertainty for concentration and dilution results from weighing error, volume error, and related inputs directly in the browser.

Review combined standard uncertainty uc, expanded uncertainty U=k·uc, the main contributors, and report-ready copy output in one place.

Calculate combined standard uncertainty uc and expanded uncertainty U=k·uc
Convert tolerance notation into standard uncertainty on the spot
Highlight the main contributors so you know what to improve
Share URLs, copy output, and local draft saving
Template
Coverage factor k
k=2 is a common approximate 95% choice. Follow your standard or internal rule when required.

What this page covers

Combine weighing and volume uncertainty into concentration uncertainty

The tool combines standard uncertainties for formulas such as C=m/V, C=(m·P)/V, and C=(m·P)/(M·V).

Convert tolerance notation into standard uncertainty

It handles certificate-style ±a(k=2), specification-style ±a, and triangular assumptions without making you do the conversion separately.

Visualize the dominant contributors

The contributor breakdown shows which factor dominates the variance so you can target improvements efficiently.

Copy output that fits reports

Switch between plain text, Markdown, CSV, and JSON and copy the exact format you need.

How to use

  1. Choose a template. Use concentration, dilution, ratio, or custom based on your calculation.
  2. Enter each factor value and its uncertainty. You can use either SD or tolerance notation.
  3. Choose the distribution and k value when needed.
  4. Review the result, the main contributors, and the report-ready copy output before pasting it into your document.

Examples

Uncertainty of mg/L from weighing and a volumetric flask

Input

m=100.00 mg ±0.10 (rectangular), V=100.00 mL ±0.08 (normal, k=2)

Output

Shows concentration, uc, U, and the contributor split between m and V.

Dilution of a standard solution

Input

C1=1000 mg/L ±5, V1=10.00 mL ±0.02, V2=100.00 mL ±0.08

Output

Shows U for the diluted concentration and which volume error matters most.

Ratios and recovery

Input

A=98.0 ±0.5, B=100.0 ±0.2

Output

Shows uncertainty for A/B or Recovery(%).

Molarity with purity and molar mass

Input

Enter m, P, M, and V together

Output

Shows the contribution from purity and molar mass as well.

Glossary

Standard uncertainty u(x)

The standard-deviation-like uncertainty associated with an input quantity x.

Combined standard uncertainty uc

The standard uncertainty of the result y after combining all input contributions.

Expanded uncertainty U

The report-facing uncertainty calculated as U = k·uc.

Sensitivity coefficient c

A coefficient showing how strongly the result changes when one input changes.

Contribution ratio

The share of the total variance attributable to one factor.

Formulas

  • Standard uncertainty conversion: u=a/k, a/√3, a/√6
  • Combined standard uncertainty: uc = √Σ(c_i·u_i)^2
  • Expanded uncertainty: U = k·uc
  • Concentration: C = m/V, (m·P)/V, (m·P)/(M·V)
  • Dilution: C2 = C1·V1/V2
  • Ratio: R = A/B

Frequently Asked Questions

I only have a ± value, not a standard deviation.

Tolerance notation can be converted into standard uncertainty when you choose a distribution assumption. The tool uses u=a/k for normal(k), u=a/√3 for rectangular, and u=a/√6 for triangular.

Which k should I use?

k=2 is common, but you should follow your standard, internal rule, or customer requirement. The tool always shows the chosen k in the result.

Can I paste this directly into a report?

Yes. Plain text, Markdown, CSV, and JSON are available, and the generated output includes assumptions, inputs, results, and the top contributors.

Can I use this when inputs are correlated?

The first release assumes independent inputs. If your inputs are correlated, the result can be under- or over-estimated.

Is it reliable for large errors or strongly nonlinear equations?

This tool uses first-order propagation. If relative uncertainties are large or the formula is strongly nonlinear, you should verify the result with another method.

Notes

  • This tool assumes independent inputs and combines uncertainty with first-order propagation.
  • If your inputs are correlated or the formula is strongly nonlinear, the result can be under- or over-estimated.
  • Automatic conversion between arbitrary concentration units is outside the first release. Enter the unit you intend to use.
  • Share URLs include free-form labels and formulas, so do not enter confidential names.

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