Calculator
Example Data Table
| Item | Delta Value (‰) | Concentration | Cost Per Mass | Note |
|---|---|---|---|---|
| Source A | -28.50 | 0.82 | 4.20 | Lower cost natural source |
| Source B | -12.20 | 1.10 | 6.50 | Higher isotope concentration |
| Sample | -20.00 | Calculated | Mixed | Unknown two-source mixture |
| Batch | Not applicable | Not applicable | 120 overhead | 1,000 mass units at 92% recovery |
Formula Used
Delta to isotope ratio: R = Rstandard × (δ ÷ 1000 + 1)
Concentration weighted source fraction: fA = CB × (δB - δM) ÷ [δM × (CA - CB) - CA × δA + CB × δB]
Second source fraction: fB = 1 - fA
Required feed mass: Feed mass = Final recovered mass ÷ (Recovery rate ÷ 100)
Finance cost: Total cost = Source A mass × Cost A + Source B mass × Cost B + Overhead
Unit cost: Unit cost = Total cost ÷ Final recovered mass
How To Use This Calculator
Select the isotope system first. Enter the standard ratio if your lab uses a custom reference. Add the delta values for Source A, Source B, and the mixed sample. Enter concentration values in matching units. Add final mass, recovery, and finance cost data. Press Calculate to view the result. Use CSV or PDF to save the report.
About Isotope Mass Balance in Finance
Isotope mass balance helps teams track material origin, purity, and process loss. It is useful when a finance report needs scientific support. Mining, food testing, fuel studies, and lab procurement can all use it. The method compares an unknown sample with two possible sources. It then estimates how much each source contributed.
Why The Calculation Matters Most
A small isotope shift can change a contract value. It can also explain yield loss or supplier variation. The calculator links isotope evidence with mass and cost data. This helps buyers, auditors, and analysts review numbers quickly. It also gives a repeatable record for internal checks.
How The Model Works Clearly
The model uses delta notation and isotope ratios. Delta values show how far a sample sits from a standard ratio. The calculator converts delta values into ratios when needed. It also applies concentration weighting. This is important because two sources may not carry the isotope at the same strength. The calculated fraction is then applied to the required feed mass.
Cost And Recovery Review Details
Finance users often need more than a source fraction. They need a cost view. This tool estimates source mass, recovered mass, material cost, overhead, and total batch cost. Recovery adjusts the feed mass. A lower recovery rate increases required input. That often raises the total cost.
Uncertainty And Control
The calculator includes an uncertainty input. It estimates how sensitive the source fraction is to isotope error. This is not a full laboratory validation. It is a planning check. It can help decide whether more testing is needed before a purchase, claim, or production decision.
Practical Use Cases
A food importer can compare honey sources. A recycler can trace mixed solvent streams. A chemical buyer can test supplier consistency. A project accountant can estimate value loss from poor recovery. The same structure works wherever isotope evidence, mass, and money meet.
Good Reporting Practice
Always keep original lab records. Use matching standards for all delta values. Check that source signatures are separated enough to support a clear estimate. Review concentration units before reporting. Export the CSV or PDF file for documentation. These files help keep calculations consistent across finance, quality, and operations teams.
FAQs
What is isotope mass balance?
It is a method that estimates how much each source contributes to a mixed sample. It uses isotope delta values, concentration data, and a mass balance equation.
Why is this calculator listed for finance?
Finance teams may need isotope evidence for supplier checks, batch costing, audits, inventory valuation, and loss analysis. The tool connects scientific fractions with material cost.
What does delta value mean?
A delta value shows the difference between a sample isotope ratio and a reference standard. It is usually reported in per mille, shown as ‰.
Why are concentrations included?
Concentration weighting improves the estimate when the two sources do not carry the target isotope at the same strength. Equal concentrations reduce the model to a simpler mixture formula.
What happens if the fraction is outside 0 to 100 percent?
The sample may not fit between the two sources. It can mean the source data is wrong, another source exists, or lab uncertainty is too high.
Can I use any mass unit?
Yes. You can use kilograms, grams, pounds, tons, or another unit. Keep all mass and cost inputs in the same unit system.
What is the uncertainty result?
It estimates how much the source fraction changes when the sample delta value moves by the entered uncertainty amount. It is a planning guide, not a full validation.
What files can I download?
You can download a CSV file for spreadsheets and a PDF file for reporting. Both include the main mass balance and finance results.