My Productivity CalcMultifactor productivity: how to calculate it, step by step
Output divided by every input, priced the same way in each period, and why it can disagree with output per hour.
Multifactor productivity is output divided by the combined cost of the inputs used to make it. Those inputs are labor, capital, energy, materials and purchased services, all priced in the same currency.
The result shows how much output each unit of total input produced. It means something only when you compare it with another period priced the same way.
What multifactor productivity measures
Labor productivity compares output with one input, the hours people worked. Multifactor productivity compares output with several inputs at once. The US Bureau of Labor Statistics groups those inputs as labor, capital, energy, materials and purchased services.
The same measure is also called total factor productivity. The Bureau of Labor Statistics replaced the term multifactor productivity with total factor productivity in November 2021.
Multifactor productivity = output ÷ (labor + capital + energy + materials + purchased services)
A measure that uses only one input, such as output per labor hour, is a partial productivity measure. The total productivity measure formula puts every input in the bottom line, as total output ÷ total input.
How to calculate multifactor productivity, step by step
- Choose the output and count it. Use a physical count if there is one product. With several products, value each one at a fixed price per unit and add them up.
- List the inputs for the same period. Labor is wages and the costs that go with them. Capital is the cost of using equipment and premises for the period, such as rent, a lease or depreciation. Energy is fuel and electricity. Materials are what goes into the product. Purchased services are work bought from outside, such as cleaning or delivery.
- Put every input in money at the same prices. Price the second period's inputs at the first period's prices, so that a price rise does not look like more input.
- Add the inputs and divide. Output ÷ total input gives output per unit of input cost.
- Compare periods. Divide the new figure by the old one, subtract 1 and multiply by 100 for the percentage change.
Worked example: a bakery buys a new oven
In this example, a bakery makes 24,000 loaves a month. Its inputs for the first month, in any currency, are below.
| Input | Month 1 | Month 2 (new oven) |
|---|---|---|
| Labor | 9,000 (600 hours) | 7,800 (520 hours) |
| Capital | 2,000 | 3,200 |
| Energy | 1,500 | 1,300 |
| Materials | 6,000 | 6,000 |
| Purchased services | 1,500 | 1,500 |
| Total input | 20,000 | 19,800 |
In month 2 the bakery leases a faster oven. Capital rises by 1,200, labor falls by 80 hours, and energy falls by 200. Output stays at 24,000 loaves. Labor costs 15 an hour in both months (9,000 ÷ 600 and 7,800 ÷ 520).
- Month 1 multifactor productivity: 24,000 ÷ 20,000 = 1.20 loaves per unit of input cost
- Month 2 multifactor productivity: 24,000 ÷ 19,800 = 1.21 (1.2121 before rounding)
- Change: (1.2121 ÷ 1.20 − 1) × 100 = 1.0%
Now compare output per labor hour for the same two months.
- Month 1: 24,000 ÷ 600 = 40.00 loaves per hour
- Month 2: 24,000 ÷ 520 = 46.15 loaves per hour
- Change: (46.15 ÷ 40.00 − 1) × 100 = 15.4%
Output per labor hour rose by 15.4%, and multifactor productivity rose by 1.0%. All of the labor saving went on the extra 1,200 of capital. The 200 fall in total input came from energy, so the oven still saved money. A report that showed only output per hour would credit the bakers with a gain the oven produced.
Worked example: when ingredient prices rise
In month 3, the bakery uses exactly the same quantities as in month 2. The price of its ingredients rises by 10%, so materials cost 6,600 instead of 6,000.
- At month 3 prices: total input 19,800 + 600 = 20,400, and 24,000 ÷ 20,400 = 1.18
- At month 2 prices: total input 19,800, and 24,000 ÷ 19,800 = 1.21
At current prices, multifactor productivity seems to fall by (1.1765 ÷ 1.2121 − 1) × 100 = 2.9%. The bakery used the same flour, the same hours and the same oven. Pricing month 3's inputs at month 2's prices removes the false fall, which is step 3 above.
Worked example: a therapy clinic
In this example, a small outpatient therapy clinic provides 600 visits in a month. Its inputs are 30,000 for staff, 6,000 for rent and treatment equipment, and 800 for energy. Supplies cost 1,200, and purchased services such as billing and cleaning cost 2,000. Total input is 30,000 + 6,000 + 800 + 1,200 + 2,000 = 40,000.
- Multifactor productivity: 600 ÷ 40,000 = 0.015 visits per unit of input cost
- Scaled to a readable number: 0.015 × 1,000 = 15 visits per 1,000 of input cost
Suppose 30 of those visits had been cancelled and the slots left empty. All inputs cost the same, so the figure falls to 570 ÷ 40,000 × 1,000 = 14.25. That is a drop of 5%, the same share as the lost visits. For the same loss in one therapist's day, see the guide on how cancellations and no-shows affect productivity.
For one therapist, employers often measure a slice of the labor input, the share of paid minutes spent on treatment. That share is worked out with the therapy productivity formula. The therapist productivity calculator works it out for one day.
Using the labor productivity calculator for a multifactor figure
The labor productivity calculator is built for the labor measure, and it can also give the multifactor figure. Enter output, labor hours, and your total input cost in the labor cost field. The line "Output per unit of labor cost" then shows output ÷ total input, rounded to two decimal places.
For the bakery's month 2, enter 24,000, 520 hours and 19,800. The calculator shows 1.21 as output per unit of labor cost, and 46.15 per hour. Ignore "Labor cost per hour" for this use, because it divides every input by labor hours. The labels still say labor, so rename the figures when you report them.
When a simpler measure fits better
Multifactor productivity suits a business or a department, where capital and materials change from period to period. For one person's working day, the inputs other than time barely move, and a time-based measure answers the question directly. For the time-based version and the five ways employers apply it, read how productivity is calculated for therapists.