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# The accurate way to calculate training volume

The need to calculate how much work you exert on your workouts becomes more and more present as you progress to complex and more advanced training systems. This process won’t be fun, especially in the beginning, but trust me it will pay off in the long run.

The easy way to calculate training volume

To estimate the overall training load, coaches and athletes use the simplified version of calculating volume-load. In this calculation you simply multiply the sets, with the repetitions and the weight lifted (equation 1)

Volume-load = Sets ∙ Reps ∙ Weight   (1)

To give an example the volume-load of 3 sets, of 10 repetitions back squats with 100kg would be:

3 ∙ 10 ∙ 100 = 3000kg

The volume-load for these 3 sets would be 3000kg. This is a nice and easy way to estimate how you progress on the same exercise.

However the problem with this calculation is that it’s not accurate when comparing different exercises and movements. For example 3 sets, of 10 repetitions with 100kg, will have the same volume load for different exercises like the back squat and the calf raises. In reality though, 10 back squats with 100kg are much harder than 10 calf raises with 100kg. Something doesn’t add up and to find out what is actually making the difference you’ll need physics.

The accurate way to calculate training volume

In physics, work is precisely defined as the product of the force exerted on an object and the distance the object moves in the direction in which the force is exerted. Quantitatively, work is defined as follows (equation 2):

Work = Force ∙ Displacement   (2)

For all these equations to work out correctly, consistent units must be used. In the International System of Units (SI, abbreviated from the French), the worldwide standard, force is measured in newtons (N), distance in meters (m), work in joules (J, i.e., newton-meters, or N·m), time in seconds (s), and power in watts (W, i.e., J/s).  As an example of applying equation 2, the net work performed when a weight is lifted is equal to the magnitude of the weight (F1 ) plus the force (F2 ) required for a desired acceleration rate multiplied by the displacement (D) in which the weight is lifted upward.

It should be noted that the weight and force direction must coincide with the direction of the displacement. The determination of this relationship is defined by the angle between the force vector and displacement vector (theta, θ). For example, the work involved in lifting a 100 kg (220-pound) barbell 2 m (6.6 feet) per repetition for 10 repetitions is calculated with the following 3 steps.

Step 1 – Weight to newtons

Determine the weight (F1 ) of the bar in SI units (newtons) by multiplying the mass of the bar in kilograms by the local acceleration due to gravity in meters per second squared. If the local acceleration due to gravity is not available, 9.8 m/s2 is a good approximation. As stated earlier, theta (θ) is the angle between the force and displacement vector, which in this case is zero:

Step 2 – Calculate the force required to move the bar

Calculate the additional force (F2 ) required to accelerate the bar mass upward at a given rate. (Force required to lower the bar in a controlled manner is calculated later.) For example, if the desired acceleration rate upward is 2 m/s2, the force required would be

Force applied to accelerate the bar upward (F2 ) = 2 m/s2 ∙ 100 kg ∙ cos 0° = 200 N

Step 3 – Do the math

Apply equation 2 to calculate the work for 10 repetitions in Joules:

Work  = (980 N + 200 N) ∙ 2 m ∙ 10 Reps = 23,600 J

This method of calculating work can be very useful for quantifying the volume of a workout. The work for each set is calculated as shown, and the total work for the whole workout is determined by addition. For free weight exercises, the vertical travel of the bar for one repetition of each exercise is measured for each individual by subtracting the height of the bar relative to the floor at its low position from the height of the bar at its high position. For weight-stack exercises, the vertical travel of the stack is measured. These measurements can be made with an empty bar or the lowest-weight plate on the stack, because the vertical distance traveled by the weight during a given exercise for an individual should be about the same regardless of the weight used.