# Cobb-Douglas Production Function Calculator

URL: https://speedycalculator.com/calculators/finance/cobb-douglas/
Last updated: 2026-10-25

> The Cobb-Douglas calculator works out output from total factor productivity, capital and labor with the Cobb-Douglas production function – plus the marginal products of capital and labor and returns to scale.

## Inputs

- Total factor productivity (A)
- Capital (K)
- Labor (L)
- Output elasticity of capital (α)
- Output elasticity of labor (β)

## Results

- Output (Q)
- Marginal product of capital
- Marginal product of labor
- Returns to scale

## Formula

```
Q = A × K^α × L^β
MPK = α × Q ÷ K; MPL = β × Q ÷ L
α + β = 1 constant, > 1 increasing, < 1 decreasing returns to scale
```

## Explanation

The Cobb-Douglas function is the workhorse of growth economics. With α ≈ 0.3–0.4 for capital, about two-thirds of national income goes to labor, which roughly matches the data for the U.S.

### How to use the Cobb-Douglas Production Function Calculator

- **Total factor productivity (A)**
- **Capital (K)**
- **Labor (L)**
- **Output elasticity of capital (α)**
- **Output elasticity of labor (β)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter total factor productivity, capital, labor and the output elasticities α and β.

### Tips

- Use real (inflation-adjusted) figures to compare across years.
- Check whether data are seasonally adjusted.
- Use the same currency and base year throughout.
- Economic models simplify reality – treat results as illustrations, not forecasts.

### Common mistakes to avoid

- Mixing nominal and real values.
- Comparing percentage changes with percentage-point changes.
- Treating correlations as causes.

### Inputs explained

FieldWhat to enterTotal factor productivity (A)A numberCapital (K)A numberLabor (L)A numberOutput elasticity of capital (α)A numberOutput elasticity of labor (β)A number

### What each result means

- **Output (Q)** = [Total factor productivity (A)]×[Capital (K)]^[Output elasticity of capital (α)]×[Labor (L)]^[Output elasticity of labor (β)]
- **Marginal product of capital** = [Output elasticity of capital (α)]×[Output (Q)]÷[Capital (K)]
- **Marginal product of labor** = [Output elasticity of labor (β)]×[Output (Q)]÷[Labor (L)]

### Example values

How the main result changes when **Total factor productivity** changes and everything else stays at the example values above:

Total factor productivity (A)Output (Q)0.75461.681.13692.521.5923.361.881,154.22.251,385.0431,846.72

## Worked example

Inputs — Total factor productivity (A): 1.5; Capital (K): 1,000; Labor (L): 500; Output elasticity of capital (α): 0.3; Output elasticity of labor (β): 0.7.

Results — **Output (Q) = 923.36**; Marginal product of capital = 0.277; Marginal product of labor = 1.2927; Returns to scale = Constant returns to scale.

## FAQ

**What is the Cobb-Douglas production function?**
Q = A K^α L^β, relating output to capital and labor.

**What do α and β mean?**
The share of output growth from a 1% increase in each input.

**What is total factor productivity?**
Output growth not explained by capital and labor – technology and efficiency.

**What formula does the Cobb-Douglas Production Function Calculator use?**
Q = A × K^α × L^β.