Ten Berge Scaling Calculator

Declared tenBerge∑C^nΔtand equivalent time under independently validated exponent, n>0. Not existing n=1Haberintegration, universal exponent, iso-effect certainty or safe exposure duration.

Description

The ten Berge concentration–time convention weights concentration using an independently validated exponent.

The ten Berge concentration–time convention weights concentration using an independently validated exponent.^[1]

An equivalent-time calculation requires that same model to apply across the compared conditions.

When to use Ten Berge Scaling Calculator

Use this tool to calculate or review the supplied observations under the stated rules. Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.

How to use Ten Berge Scaling Calculator and understand its results

Establish the chemical, exposure route, endpoint, measurement basis and independently applicable assay or assessment reference.
Enter actualIntervalConcentrations, actualIntervalMinutes, callerIndependentlyValidatedTenBergeExponent, callerComparedConcentration, using the field meanings and rules below, then run the tool.
Read result.conditionalPowerWeightedConcentrationTime, result.conditionalEquivalentMinutesAtCallerConcentration. Use the units and subtraction order below to interpret each value; retain negative differences where returned.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
actualIntervalConcentrations	Actual interval concentrations	list of number	Required
actualIntervalMinutes	Actual interval minutes	list of number	Required
callerIndependentlyValidatedTenBergeExponent	Caller independently validated ten berge exponent	number	Required
callerComparedConcentration	Caller compared concentration	number	Required

Supply nonempty aligned nonnegative concentrations and positive durations, a positive independently applicable exponent and a positive comparison concentration. Sum concentration raised to the exponent times duration; divide by the comparison concentration raised to that exponent for equivalent duration. Reject nonfinite outputs. The exponent and applicability are external inputs.

inventory=Σ(C_i^n×duration_i); equivalentDuration=inventory/comparisonConcentration^n

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Qualified observed calculation or explicit reference	object
result.conditionalPowerWeightedConcentrationTime	Sum of concentration raised to the supplied exponent times interval minutes.	number
result.conditionalEquivalentMinutesAtCallerConcentration	Power-weighted inventory divided by comparison concentration raised to the same exponent.	number

json

{
  "input": {
    "actualIntervalConcentrations": [
      1,
      2
    ],
    "actualIntervalMinutes": [
      2,
      3
    ],
    "callerIndependentlyValidatedTenBergeExponent": 2,
    "callerComparedConcentration": 2
  },
  "output": {
    "result": {
      "conditionalPowerWeightedConcentrationTime": 14,
      "conditionalEquivalentMinutesAtCallerConcentration": 3.5
    }
  }
}

Limitations and assumptions

Chemical identity, route, assay, exposure basis and reference applicability are caller-established. The output supplies no causal conclusion, universal toxicity threshold or authoritative regulatory determination.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use REL TWA Calculator: A recommended-exposure-limit average needs the adopted NIOSH reference and shift basis. For a complementary comparison, use PEL TWA Calculator: A permissible-exposure-limit average belongs to a jurisdiction, edition and defined shift.

References

Ten Berge Scaling Calculator — tool.io

Similar or alternative tools

REL TWA Calculator
A recommended-exposure-limit average needs the adopted NIOSH reference and shift basis.
PEL TWA Calculator
A permissible-exposure-limit average belongs to a jurisdiction, edition and defined shift.