ثابت الالتواء

${\displaystyle J_{zz}=J_{xx}+J_{yy}={\frac {\pi r^{4}}{4}}+{\frac {\pi r^{4}}{4}}={\frac {\pi r^{4}}{2}}}$^[2]

${\displaystyle J\approx {\frac {\pi a^{3}b^{3}}{a^{2}+b^{2}}}}$^[3][4]

${\displaystyle J\approx \,2.25a^{4}}$^[5]

${\displaystyle J\approx \beta ab^{3}}$

a/b	${\displaystyle \beta }$
1.0	0.141
1.5	0.196
2.0	0.229
2.5	0.249
3.0	0.263
4.0	0.281
5.0	0.291
6.0	0.299
10.0	0.312
${\displaystyle \infty }$	0.333

^[6] وبالتالي يمن استخدام هذة المعادلة بنسبة خطأ لا تزيد عن 4%

${\displaystyle J\approx ab^{3}\left({\frac {1}{3}}-0.21{\frac {b}{a}}\left(1-{\frac {b^{4}}{12a^{4}}}\right)\right)}$^[3]

${\displaystyle J={\frac {1}{3}}Ut^{3}}$^[7]