# Formula for distance? **URL:** \ **Category:** Factual Questions\ **Created:** [September 17, 2003, 12:29am UTC](https://boards.straightdope.com/t/formula-for-distance/202055 "2003-09-17T00:29:13Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![Supernate](https://avatars.discourse-cdn.com/v4/letter/s/ecc23a/32.png) [@Supernate](https://boards.straightdope.com/u/Supernate)\ **Post date:** [September 17, 2003, 12:29am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/1 "2003-09-17T00:29:13Z")
I was sitting inside at a house on a bay, looking across the bay at another house that I suspect is about a mile away. I noticed that the house across the bay had a window similar in size of the window I was looking though and it got me thinking. Suppose I took a 12" ruler out, placed it a fixed distance from my eye so that the window I was looking out _appeared_ to be 12" high. Now, if the window across the bay now appears to be 1/4" high, **is there a way to tell how far away the window across the bay is from just these two numbers?** Or in other words, is there a known formula for the appearance of diminishing size related to distance? ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [September 17, 2003, 1:18am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/2 "2003-09-17T01:18:46Z")
Yes, it is extremely easy. The ratio (distance eye-ruler) / (ruler measure) is the same as (distance eye - object) / (object measure) therefore: Distance to object = (distance eye - ruler) \* (object size) / (ruler measure) ---
**Author:** ![FairDink](https://avatars.discourse-cdn.com/v4/letter/f/ed8c4c/32.png) [@FairDink](https://boards.straightdope.com/u/FairDink)\ **Post date:** [September 17, 2003, 1:41am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/3 "2003-09-17T01:41:59Z")
Dunno. But I know in software such as games, they take into consideration the angle of visibility. In other words, the size an object appears is calculated based on distance and the angle (cone) of visibility. The formulas, that i have seen, are based on matricies and many other fun things like that. [Just one example of things to take into consideration.](http://gameprogrammer.com/fractal.html#ptI) ---
**Author:** ![FairDink](https://avatars.discourse-cdn.com/v4/letter/f/ed8c4c/32.png) [@FairDink](https://boards.straightdope.com/u/FairDink)\ **Post date:** [September 17, 2003, 1:48am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/4 "2003-09-17T01:48:41Z")
Of-course if you knew 1. your distance from ruler, 2. your height from base of window and 3. the angle from eye to top of ruler, then it is a matter of simple geometry. ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [September 17, 2003, 3:51am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/5 "2003-09-17T03:51:06Z")
Well FairDink, he’s sittin’ there looking at it, so we know already that’s it’s in his cone of visibility, and the problem is greatly simplified. Supernate, Google on “similar triangles”. ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 17, 2003, 4:10am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/6 "2003-09-17T04:10:14Z")
quote **is there a way to tell how far away the window across the bay is from just these two numbers?** Actually **Supernate** from JUST those two numbers you cannot determine the distance to the window across the bay. You will need to know a few other things in order to determine the distance. Granted you can measure these variables since they are in proximity. BUT in response to the OP, sorry ya gotta have more than that. ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [September 17, 2003, 4:16am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/7 "2003-09-17T04:16:09Z")
> [@](#): > > \*Originally posted by t-keela \* > \*\*quote **is there a way to tell how far away the window across the bay is from just these two numbers?** > > Actually **Supernate** from JUST those two numbers you cannot determine the distance to the window across the bay. You will need to know a few other things in order to determine the distance. Granted you can measure these variables since they are in proximity. > > BUT in response to the OP, sorry ya gotta have more than that. \*\* Did you read the OP? Did you read my response? He has three numbers and enough information to solve the problem very simply as I have explained. I wish people would read what’s been posted. It seems many people do a drive-by spouting the first thing that comes to mind, without bothering to pay attention to what has been said. ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [September 17, 2003, 4:20am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/8 "2003-09-17T04:20:17Z")
> [@](#): > > \*Originally posted by sailor \* > \*\*Did you read the OP? Did you read my response? He has three numbers and enough information to solve the problem very simply as I have explained. \*\* Umm…hello?? > [@](#): > > _From the OP:_ > is there a way to tell how far away the window across the bay is from just these **two numbers**? You were saying? ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 17, 2003, 4:27am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/9 "2003-09-17T04:27:15Z")
I did read everything **Sailor**. What the OP asked was “is there a way to tell how far away the window across the bay is from **just** these two numbers?” bolding mine I read that to mean…can I get the answer I want with these two numbers ONLY. Then the OP asked another question “is there a known formula for the appearance of diminishing size related to distance?” Others such as yourself answered the second part of the OP. That’s great, but maybe the guy wanted an answer to the first question as well. And the last part, your comment, **" I wish people would read what’s been posted. It seems many people do a drive-by spouting the first thing that comes to mind, without bothering to pay attention to what has been said."** wasn’t necessary ☹ There are several ways to determine distance BTW. ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 17, 2003, 4:29am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/10 "2003-09-17T04:29:36Z")
Thanks **Q.E.D.** ---
**Author:** ![Q.E.D](https://avatars.discourse-cdn.com/v4/letter/q/51bf81/32.png) [@Q.E.D](https://boards.straightdope.com/u/Q.E.D)\ **Post date:** [September 17, 2003, 4:35am UTC](https://boards.straightdope.com/t/formula-for-distance/202055/11 "2003-09-17T04:35:42Z")
Welcome 🙂