How to Find the Percentage Between Two Ratios?

Question

If 0% = 900 and 100% = 1800, how do you find the percentage of 1200?

Question: 1200 = ?%

ms = milliseconds

In other words, on a timeline from 0ms to 1800ms, if an object weren't to move until 900ms passed, and it would have moved exactly 0% during that time. What percent would it have moved until it stopped at 1200ms?

This formula would be used on a website :)

There is not a unique answer to your question as the acceleration has not been specified. — Andrew Chin, Jan 27 '21 at 11:58
@AndrewChin This is not needed to solve the problem thank you for your interest :) — twominds, Jan 27 '21 at 11:59
If the scale is linear, then $1200$ would be $\frac{1200-900}{1800-900} = \frac{1}{3} \approx 33.3 %$. — Toby Mak, Jan 27 '21 at 12:16
Similar problem: https://math.stackexchange.com/questions/3355027/a-function-or-a-factor-to-scale-a-list-of-real-numbers-from-one-range-to-another/3355071#3355071 — Matti P., Jan 27 '21 at 12:17
Does this answer your question? A function or a factor to scale a list of real numbers from one range to another. We have over 1 million questions on this site, so it is likely that someone has asked the same question as you. Before asking, please search your question on Approach0 to see if there are any duplicates. — Toby Mak, Jan 27 '21 at 12:18
@TobyMak That would be the answer, thank you :) In my situation, the lerp cannot be defined. So I apologize for any confusion. And thank you for your resources. — twominds, Jan 27 '21 at 12:24
Linear interpolation. This is what is calculated based on the browser, screen width, and height ratio, and OS. So it's the acceleration or scale I believe you're referring to? Your formula plugged right into my code, thx :) — twominds, Jan 27 '21 at 12:27
@TobyMak Heres your formula in action https://imgur.com/xXYhHkn — twominds, Jan 27 '21 at 12:58

score 2 · Accepted Answer · answered Jan 27 '21 at 13:35

The percentage can be expressed as a ratio of lengths.

The longer length which represents $100$ percent is $1800 - 900 = 900$ units long, and the shorter length is $1200 - 900 = 300$ units long. Therefore, $1200$ is $\frac{300}{900} = \frac{1}{3}$ of the way to $1800$, which is around $33.3$ percent.

This is equivalent to linear interpolation as you have mentioned: the gradient of the line between the two endpoints, and the gradient of the point $(x,1200)$ and one endpoint must be equal.

How to Find the Percentage Between Two Ratios?

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