How do I preserve the ratio between values when converting number ranges?

Preserving Ratio When Converting Number Ranges

In the realm of data manipulation, the need often arises to convert values from one range to another while maintaining their relative ratios. This can be particularly useful when compressing data or mapping values between different scales.

Let's consider the task of converting a range of values from -16000.00 to 16000.00 to a more manageable integer range of 0-100. We want to ensure that the conversion preserves the ratio between the original values.

The key to achieving this ratio preservation lies in the following formula:

NewValue = (((OldValue - OldMin) * (NewMax - NewMin)) / (OldMax - OldMin)) + NewMin

where:

• OldValue is the original value within the old range
• OldMin and OldMax are the minimum and maximum values of the old range
• NewMax and NewMin are the maximum and minimum values of the new range

To break it down further:

• We calculate the normalized ratio of the OldValue within the old range: (OldValue - OldMin) / (OldMax - OldMin)
• We multiply this ratio by the size of the new range: (NewMax - NewMin)
• We shift this result by the minimum of the new range: NewMin

This formula ensures that the ratio between values within the old range is preserved within the new range.

For example, if OldValue is 8000.00, OldMin is -16000.00, OldMax is 16000.00, NewMax is 100, and NewMin is 0, NewValue would be calculated as follows:

NewValue = (((8000.00 - (-16000.00)) * (100 - 0)) / (16000.00 - (-16000.00))) + 0
= (((24000.00) * (100)) / (32000.00)) + 0
= 75.00

Thus, 8000.00 in the old range corresponds to 75.00 in the new range, preserving the relative ratio between these values. This formula can be further customized to handle cases where the old range is zero or the desired new range does not start at zero.

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