We propose a new method which combines experiments with numerical calculations to determine the capillary constant and the capillary contact angle. We measure the ascent of the liquid at the interior and at the exterior of a circular transparent tube. In contrast to known methods we do not assume that the contact angle is known. Assuming the interior contact angle is equal to the exterior angle, we find the capillary constant of the given liquid from the fact that the surface tensions of the interior and the exterior surfaces are equal. Dipping a cylindrical wire with constant circular cross section into a liquid with known surface tension we can determine the contact angle between the given liquid and the material from which the wire is made.