The most useful paper is Bih et al.¹.

Where l is length, w is width, h is height and r is radius.

When using ultrasound, the radius is clearly not measured and it is the diameter that is measured (so we need to divide by 2 in our formulas). Also, the diameter is not equal in both directions (so we have three measurements, a, b, and c, or if you want, l, w, and h - I will use these interchangeably). Therefore, there are slight modifications as follows.

The volume of an ellipsoid is ⁴⁄₃π(^a⁄₂)(^b⁄₂)(^c⁄₂) where a, b and c are the dimensions that you would measure on ultrasound. The volume of a cylinder (ellipsoid cylinder used by Bih et al) would be π(^a⁄₂)(^b⁄₂)h.

The final shape used by Bih et al is is a triangular prism where the volume is width x depth x height/2.

Where l is length, w is width, h is height, d is depth (to eliminate confusion of length vs height), and r is radius.

The coefficients are obvious e.g. for a sphere 0.52 = (⁴⁄₃π)/2³

Bih et al demonstrated that if we estimate the approximate bladder shape, we could use coefficients close to these to give more accurate bladder volumes. Of course the exact coefficients for perfect cuboids and ellipsoids were not the most reflective of bladder shape. 0.72 was determined the most appropriate for the whole dataset (including all shapes). For cuboid shaped bladders the most appropriate coefficient was 0.89, for ellipsoid cylinders, 0.81, and for triangular prisms 0.66.

References

1. L I Bih, C. C. H. Bladder shape impact on the accuracy of ultrasonic estimation of bladder volume. Arch. Phys. Med. Rehabil. 79, 1553–6 (1999).
2. Kuzmić, A. C., Brkljačić, B. & Ivanković, D. The impact of bladder shape on the ultrasonographic measurement of bladder volume in children. Pediatr. Radiol. 33, 530–534 (2003).