\displaystyle \kappa(t)=\dfrac{|r'(t)\times r''(t)|}{|r'(t)|^{3}} 또는 원의 경우 \displaystyle \kappa = \dfrac{1}{R}.

1. \displaystyle r'(t): \langle -3\sin t, 3\cos t, 4\rangle. \displaystyle |r'(t)|=\sqrt{9\sin^{2}t+9\cos^{2}t+16}=\sqrt{25}=5.

2. \displaystyle r''(t): \langle -3\cos t,-3\sin t,0\rangle.

3. 외적: \displaystyle r'(t)\times r''(t)=\langle 12\sin t,-12\cos t,9\rangle.

4. 외적 크기: \displaystyle |r'(t)\times r''(t)|=\sqrt{144\sin^{2}t+144\cos^{2}t+81}=\sqrt{144+81}=\sqrt{225}=15.

5. 곡률 \kappa: \displaystyle \kappa(t)=\dfrac{15}{5^{3}}=\dfrac{15}{125}=\dfrac{3}{25}.