CHEM TOOLS
Measurement Uncertainty Reiknivél

Measurement Uncertainty Reiknivél (Concentration from Weighing and Volume)

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

Yfirferð combined standard uncertainty uc, expanded uncertainty U=k·uc, the main contributors, and skýrsla-ready copy úttak 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 úttak, and local draft saving
Sniðmát
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 verkfæri 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 úttak that fits skýrslas

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

How to use

  1. Choose a sniðmát. 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. Yfirferð the niðurstaða, the main contributors, and the skýrsla-ready copy úttak before pasting it into your document.

Examples

Uncertainty of mg/L from weighing and a volumetric flask

Inntak

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

Úttak

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

Dilution of a standard solution

Inntak

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

Úttak

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

Ratios and recovery

Inntak

A=98.0 ±0.5, B=100.0 ±0.2

Úttak

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

Molarity with purity and molar mass

Inntak

Enter m, P, M, and V together

Úttak

Shows the contribution from purity and molar mass as well.

Glossary

Standard uncertainty u(x)

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

Combined standard uncertainty uc

The standard uncertainty of the niðurstaða y after combining all inntak contributions.

Expanded uncertainty U

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

Sensitivity coefficient c

A coefficient showing how strongly the niðurstaða changes when one inntak changes.

Contribution ratio

The share of the total variance attributafla 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 verkfæri 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 verkfæri always shows the chosen k in the niðurstaða.

Can I paste this directly into a skýrsla?

Yes. Plain text, Markdown, CSV, and JSON are available, and the generated úttak includes assumptions, inntaks, niðurstaðas, and the top contributors.

Can I use this when inntaks are correlated?

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

Is it reliable for large errors or strongly nonlinear equations?

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

Athugasemdir

  • This verkfæri assumes independent inntaks and combines uncertainty with first-order propagation.
  • If your inntaks are correlated or the formula is strongly nonlinear, the niðurstaða 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.