# figuring out the acreage of a circle **URL:** \ **Category:** Factual Questions\ **Created:** [September 25, 2007, 9:15pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481 "2007-09-25T21:15:45Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [September 25, 2007, 9:15pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/1 "2007-09-25T21:15:45Z")
Sorry to be an idiot – I did the math, but I don’t trust myself, and I can’t find an online converter to check it against. I need the acreage equivalent of a circle that’s five miles in diameter. Area is Pi r[super]2[/super], so pi x5[super]2[/super], or pi x 25, or roughly 78.5 square miles, which would be a tad over 50K acres. Is that right? ETA: and how the hell do you do superscripts? ---
**Author:** ![Randy\_Seltzer](https://avatars.discourse-cdn.com/v4/letter/r/ee7513/32.png) [@Randy\_Seltzer](https://boards.straightdope.com/u/Randy_Seltzer)\ **Post date:** [September 25, 2007, 9:18pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/2 "2007-09-25T21:18:58Z")
[QUOTE=twickster] Sorry to be an idiot – I did the math, but I don’t trust myself, and I can’t find an online converter to check it against. I need the acreage equivalent of a circle that’s five miles in diameter. Area is Pi r[super]2[/super], so pi x5[super]2[/super], or pi x 25, or roughly 78.5 square miles, which would be a tad over 50K acres. Is that right? ETA: and how the hell do you do superscripts? [/QUOTE] Well your first problem is that r isn’t 5; it’s 2.5. So 2.5 squared is 6.25. Times pi is about 19.6 square miles. ETA: And 19.6 sq miles = about 12.5k acres. ---
**Author:** ![corkboard](https://avatars.discourse-cdn.com/v4/letter/c/e9bcb4/32.png) [@corkboard](https://boards.straightdope.com/u/corkboard)\ **Post date:** [September 25, 2007, 9:20pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/3 "2007-09-25T21:20:10Z")
On preview: what he said. As for superscripts, no idea. ---
**Author:** ![StGermain](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/stgermain/32/2868_2.png) [@StGermain](https://boards.straightdope.com/u/StGermain)\ **Post date:** [September 25, 2007, 9:20pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/4 "2007-09-25T21:20:23Z")
I’m no geometry whiz, but the radius is half the diameter. So 3.1415 X 2.5 sq (6.25) = 19.63. StG ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [September 25, 2007, 9:21pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/5 "2007-09-25T21:21:43Z")
[QUOTE=Randy Seltzer] Well your first problem is that r isn’t 5; it’s 2.5. [/QUOTE] :smack: This is why I wanted someone to check what I was doing! (My standard disclaimer is that I’m number dyslexic. No. Seriously.) ---
**Author:** ![Oredigger77](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/oredigger77/32/3181_2.png) [@Oredigger77](https://boards.straightdope.com/u/Oredigger77)\ **Post date:** [September 25, 2007, 9:21pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/6 "2007-09-25T21:21:46Z")
ya what they said ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [September 25, 2007, 9:23pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/7 "2007-09-25T21:23:15Z")
No, wait, sorry. The RADIUS of the circle is 5 miles, not the diameter. God, could we just pretend I never started this? ---
**Author:** ![Chez\_Guevara](https://avatars.discourse-cdn.com/v4/letter/c/aeb1de/32.png) [@Chez\_Guevara](https://boards.straightdope.com/u/Chez_Guevara)\ **Post date:** [September 25, 2007, 9:31pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/8 "2007-09-25T21:31:41Z")
N[sup]o[/sup]. ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [September 25, 2007, 9:32pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/9 "2007-09-25T21:32:57Z")
[QUOTE=Chez Guevara] N[sup]o[/sup]. [/QUOTE] Sup, super, whatever. 😛 ---
**Author:** ![Jodi](https://avatars.discourse-cdn.com/v4/letter/j/7feea3/32.png) [@Jodi](https://boards.straightdope.com/u/Jodi)\ **Post date:** [September 25, 2007, 9:40pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/10 "2007-09-25T21:40:22Z")
[QUOTE=twickster] No, wait, sorry. The RADIUS of the circle is 5 miles, not the diameter. [/QUOTE] Well, we can’t figure it out unless you also give us the ulna. _Duh!_ ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [September 25, 2007, 9:40pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/11 "2007-09-25T21:40:27Z")
If the radius of the circle was five miles, your first calculation was OK. (I kept an additional decimal, so I got 78.54.) Your self-check for that is also pretty easy. A radius of 5 is a diameter of 10, of course. A circle with a diameter of 10 would fit into a square of 10 units to each side with a tangent on the mid-point of every 10 unit side line segment. A square that is 10 x 10 would be 100 square units, so a circle of 78.54 units for a square with the corners knocked off seems realistic. ---
**Author:** ![Projammer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/projammer/32/559_2.png) [@Projammer](https://boards.straightdope.com/u/Projammer)\ **Post date:** [September 25, 2007, 9:41pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/12 "2007-09-25T21:41:39Z")
[Google calculator](http://www.google.com/intl/en/help/features.html#calculator) is your friend. Your square mile calculation is correct. 78.5398 square miles. Hit Google calculator and feed it ‘78.5398 square miles in acres’ and get 78.5398 (square miles) = 50 265.472 acres for your result. ---
**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 25, 2007, 11:54pm UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/13 "2007-09-25T23:54:28Z")
[QUOTE=twickster] ETA: and how the hell do you do superscripts? [/QUOTE] 2[sup]99[/sup] = 2[sup]99[/sup] ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [September 26, 2007, 12:01am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/14 "2007-09-26T00:01:26Z")
Now that the question is answered, may I point out that _radius_ is the only word for _radius_? ---
**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 26, 2007, 12:08am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/15 "2007-09-26T00:08:39Z")
[QUOTE=Mangetout] Now that the question is answered, may I point out that _radius_ is the only word for _radius_? [/QUOTE] [Semidiameter](http://cancerweb.ncl.ac.uk/cgi-bin/omd?semidiameter). 😛 ---
**Author:** ![twickster](https://avatars.discourse-cdn.com/v4/letter/t/ec9cab/32.png) [@twickster](https://boards.straightdope.com/u/twickster)\ **Post date:** [September 26, 2007, 12:09am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/16 "2007-09-26T00:09:08Z")
[QUOTE=tomndebb] Your self-check for that is also pretty easy… [/QUOTE] Are you mocking me, sir? Given how confused I got just asking the question, I am forced to assume you are. ☹ ---
**Author:** ![danceswithcats](https://avatars.discourse-cdn.com/v4/letter/d/9e8a1a/32.png) [@danceswithcats](https://boards.straightdope.com/u/danceswithcats)\ **Post date:** [September 26, 2007, 12:15am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/17 "2007-09-26T00:15:51Z")
Just in case you’d like to offer the answer in metric units, that would equate to 20341.7297 hectares. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [September 26, 2007, 12:19am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/18 "2007-09-26T00:19:36Z")
[QUOTE=Q.E.D.] [Semidiameter](http://cancerweb.ncl.ac.uk/cgi-bin/omd?semidiameter). 😛 [/QUOTE] I’m guessing that word was specifically made up for this purpose - like those new words that rhyme with orange. ---
**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 26, 2007, 12:23am UTC](https://boards.straightdope.com/t/figuring-out-the-acreage-of-a-circle/420481/19 "2007-09-26T00:23:55Z")
[QUOTE=Mangetout] I’m guessing that word was specifically made up for this purpose - like those new words that rhyme with orange. [/QUOTE] Heh. Actually, it’s an [actual word](http://www.answers.com/topic/semidiameter), with a slightly different meaning; apparently corrupted by my previous source.