The physical quantities that have the same dimensional formula as work are energy and torque. The dimensional formula of work is [ML2T−2][ML^2T^{-2}][ML2T−2], which is identical to the dimensional formula of energy and torque. Work is defined as force times displacement, and its dimensional formula is derived as follows:
- Force has the dimensional formula [MLT−2][MLT^{-2}][MLT−2]
- Displacement has the dimensional formula [L][L][L]
- Multiplying these gives the dimensional formula of work: [ML2T−2][ML^2T^{-2}][ML2T−2]
Energy shares the same dimensional formula because it is equivalent to work in terms of dimensions. Torque also has the same dimensional formula as it is force times lever arm distance, similarly resulting in [ML2T−2][ML^2T^{-2}][ML2T−2]. Power, however, differs with the formula [ML2T−3][ML^2T^{-3}][ML2T−3] as it is work done per unit time.
