The full range is from to . The distance between these is , which is .

The current value of the slider is .This is , that is, larger than the minimum possible value.

We are interested in the ratio . A calculator shows that . We want to express as a percentage. To do that, we multiply by . The result is . So the required percentage setting for is .

Since we will not always be dealing with the setting , let's generalize a little. Suppose that the slider setting is . (In your question, .) Assume that .

Then the distance from to the minimum is The ratio of this distance to the full distance is

To turn this into a percentage, multiply by . The answer is

Reality check: It is quite easy to make mistakes, I have done it hundreds of times. So let's see what answer we get from the above formula when . Substitute for . We get . Good. Let's see what answer we get if we put . Substitute. We get . In general, spot checks of this kind do not guarantee that a formula is correct, but they are good evidence that we have not made a horrible blunder. (In linear cases, such as this one, two spot checks in fact do guarantee correctness.)

Now let us adjust the formula so that we can deal with a different situation, where the minimum setting is and the maximum setting is . Let . Then the percentage that corresponds to the setting is given by The reasoning that gives this formula is exactly the same as the one we used for the concrete numbers you supplied.

Now that we have a formula that gives the percentage when we know the setting , we can use a little algebra to get a formula that gives the setting if we are told the desired percentage . If you have need of such a formula, and have difficulty deriving it, please leave a message.

I put together this function to calculate it. It also gives the ability to set a mid way 100% point that then goes back down.

Usage

//[] = optional
rangePercentage(input, minimum_range, maximum_normal_range, [maximum_upper_range]);

rangePercentage(250, 0, 500); //returns 50 (as in 50%)

rangePercentage(100, 0, 200, 400); //returns 50
rangePercentage(200, 0, 200, 400); //returns 100 
rangePercentage(300, 0, 200, 400); //returns 50 

The function

function rangePercentage (input, range_min, range_max, range_2ndMax){

    var percentage = ((input - range_min) * 100) / (range_max - range_min);

    if (percentage > 100) {

        if (typeof range_2ndMax !== 'undefined'){
            percentage = ((range_2ndMax - input) * 100) / (range_2ndMax - range_max);
            if (percentage < 0) {
                percentage = 0;
            }
        } else {
            percentage = 100;
        }

    } else if (percentage < 0){
        percentage = 0;
    }

    return percentage;
}

Hi Jeovany, thanks for the response.

the problem with Vlookup is it is reliant on the data in the table rather than a calculation, which would be more accurate. As I said, the percentage I am looking for any value between number 1 and15-million. That said if I use increments of 10,000 it is a manageable 1500 lines to 15 million. So I can use the true function accurately enough here. Thanks for the advice.

clive

Find $8\%$ of $30-(-5)$. That is $$\frac{8}{100}\times 35=m.$$ Then what you want is $-5+m$.