Ratio, Proportion & Scaling Validator — Error, Scaling Factor and Missing Value Calculator
Calculate normalized ratio error, mean scaling factor and solved value using A, B, C and D based on proportion validation.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Proportional values
Validation settings
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
ratio error formula:
ratio error is calculated as:
A/B = A / B
C/D = C / D
ε = |((A/B) − (C/D)) / (|A/B| > 1e−12 ? A/B : 1)|
scaling factor formula:
k1 = C / A, when A ≠ 0
k2 = D / B, when B ≠ 0
k = (k1 + k2) / 2, when both k1 and k2 are available
k = k1 or k2, when only one scaling factor is available
solved value formulas:
- A = (B · C) / D, when A is unknown and D ≠ 0
- B = (A · D) / C, when B is unknown and C ≠ 0
- C = (A · D) / B, when C is unknown and B ≠ 0
- D = (B · C) / A, when D is unknown and A ≠ 0
where:
- A — first value in the first ratio (–)
- B — second value in the first ratio (–)
- C — first value in the second ratio (–)
- D — second value in the second ratio (–)
- ε — normalized ratio error (–)
- k — mean scaling factor (–)
- X — solved value (–)
- t — tolerance (%)
When to use this calculator
When to use this calculator:
- Validate whether two value pairs keep the same proportion through A/B and C/D comparison.
- Solve exactly one missing value in a four-value proportion.
- Check whether linear scaling gives consistent scaling factors from both value pairs.
- Check whether inverse scaling satisfies the selected tolerance condition.
- Detect sign inconsistency between corresponding proportional values.
- Flag unknown unit consistency when the unit relationship is not confirmed.
How to interpret the result
Ratio error is defined as the normalized difference between the first value pair ratio and the second value pair ratio.
Mean scaling factor depends on the scaling from the first value to the third value and from the second value to the fourth value. When both scaling paths produce the same factor, the scaling consistency error is zero.
- Safe — proportional deviation is ≤ tolerance, scaling consistency error is ≤ tolerance / 100 when available, relative cross-product error is ≤ tolerance / 100 when available, no physical warning exists, and unit consistency is confirmed.
- Warning — proportional deviation is within 2 × tolerance, or all numeric checks are within tolerance but unit consistency is unknown.
- Unsafe — proportional deviation is greater than 2 × tolerance.
- Invalid — mode, scaling type, tolerance, required values, denominator values, or solve-mode input count violates the calculation requirements.
The result is used to evaluate whether two value pairs preserve the selected proportional or scaling relationship within the selected tolerance.
Calculation example
Example:
A user wants to solve one missing value in a proportional pair. The selected mode is Solve missing value, scaling type is Linear scaling, unit consistency is Consistent, and tolerance is 1%.
- B = 5
- C = 60
- D = 15
- A is unknown
X = A = (5 · 60) / 15 = 20
A/B = 20 / 5 = 4 and C/D = 60 / 15 = 4, so ε = 0 and k = 3.
Assumptions and limitations
- All provided proportional values must be finite real numbers.
- The second value of the first ratio and the second value of the second ratio must not be zero.
- Validation mode requires all four proportional values.
- Solve mode requires exactly one unknown proportional value.
- Default tolerance is 1% when no tolerance is provided.
- Unknown unit consistency produces a warning even when numeric proportional checks pass.