Približki za obseg elipse z glavnima polosema a in b:
(Kepler, 1609)

(Euler, 1773)
![{\displaystyle o\approx \pi \left[{\frac {a+b}{2}}+{\sqrt {\frac {a^{2}+b^{2}}{2}}}\right]\,\!,}](//wikimedia.org/api/rest_v1/media/math/render/svg/abb6324843f8035c4e8abd8e9b22e34b9c2fd731)
![{\displaystyle o\approx \pi \left[{\frac {3}{2}}(a+b)-{\sqrt {ab}}\right]\,\!}](//wikimedia.org/api/rest_v1/media/math/render/svg/cca12f290b84d4e2ed6746bfcff1e669394a0abf)
ali:

Vsak približek je točnejši od predhodnega.
Dobra približka je leta 1914 dal Ramanudžan:
![{\displaystyle o\approx \pi \left[3(a+b)-{\sqrt {(3a+b)(a+3b)}}\right]=\pi (a+b)\left[3-{\sqrt {4-h}}\right]\,\!,}](//wikimedia.org/api/rest_v1/media/math/render/svg/835354480bc9c1bd90572f45d6846ae662a2235e)
![{\displaystyle o\approx \pi (a+b)\left[1+{\frac {3\left({\frac {a-b}{a+b}}\right)^{2}}{10+{\sqrt {4-3\left({\frac {a-b}{a+b}}\right)^{2}}}}}\right]=\pi \left(a+b\right)\left[1+{\frac {3h}{10+{\sqrt {4-3h}}}}\right]\,\!.}](//wikimedia.org/api/rest_v1/media/math/render/svg/263256bcbbb9e6485fc8782bcf3435ff8f291018)
kjer je h parameter:

Tudi tukaj je drugi približek točnejši. Malo manj točen približek je med letoma 1904 in 1920 dal Lindner:
![{\displaystyle o\approx \pi (a+b)\left[1+{\frac {h}{8}}\right]^{2}\,\!.}](//wikimedia.org/api/rest_v1/media/math/render/svg/5bfa0b11eb69b023618b39502e62b5b02ceff845)
Obseg elipse s parametrom λ je:
![{\displaystyle o=\pi (a+b)\left[1+{\frac {\lambda ^{2}}{4}}+{\frac {\lambda ^{4}}{64}}+{\frac {\lambda ^{6}}{256}}+\cdots \right]=\pi (a+b)\left[1+\sum _{n=1}^{\infty }\left({\frac {(2n-2)!}{n!(n-1)!2^{2n-1}}}\right)^{2}\lambda ^{2n}\right]\,\!,}](//wikimedia.org/api/rest_v1/media/math/render/svg/479ca192a53c3afe8a85967c5bbf875e499f861f)
oziroma s parametrom h:
![{\displaystyle o=\pi (a+b)\left[1+{\frac {h}{4}}+{\frac {h^{2}}{64}}+{\frac {h^{3}}{256}}+{\frac {25h^{4}}{16384}}+{\frac {49h^{5}}{65536}}+\cdots \right]=\pi (a+b)\sum _{n=0}^{\infty }{{1 \over 2} \choose n}^{2}h^{n}\,\!,}](//wikimedia.org/api/rest_v1/media/math/render/svg/cc8daa4652a7ac827658f86c041165fa46f1f0ab)
približek pa (Hudsonova enačba, 1917):

Hudsonovo enačbo po navadi pišejo s parametrom L:

![{\displaystyle o\approx {\frac {\pi }{4}}(a+b)\left[3(1+L)+{\frac {1}{1-L}}\right]\,\!.}](//wikimedia.org/api/rest_v1/media/math/render/svg/4f5e0e5716ef938a88692638c969ba742ed43135)