Bellman Equation Calculator

How to solve the bellman equation quickly? The Bellman Equation calculator is here to help you. This tool can help you to compute the values of the Bellman equation, which is essential in dynamic programming and reinforcement learning.

For calculation enter your values into calculator as, reward, discount factor and value of next state to determine value function.

Bellman Equation Calculator

Enter any 3 values to calculate the missing variable

What is the Bellman Equation?

The Bellman equation, named after Richard Bellman, is a recursive equation used to calculate the optimal policy in a Markov decision process. It helps in determining the best action to take in each state to maximize the cumulative reward.

How to Use the Calculator

Using the Bellman Equation Calculator is simple. Here’s how:

Input Fields:

    • Reward (R): Immediate reward received from the current state.
    • Discount Factor (γ): Represents the importance of future rewards compared to present rewards.
    • Value of Next State (V): The value of the next state.
    • Value Function (V):* The value function of the current state.

Example Input Values:

    • Reward (R): 10
    • Discount Factor (γ): 0.9
    • Value of Next State (V): 20

How to Calculate Using the Bellman Equation

To calculate the value function using the Bellman Equation, follow these steps:

Formula: V∗(s)=R(s)+γ∗V(s′)


Variable Description
V*(s) Value function of the current state (s)
R(s) Immediate reward received from the current state (s)
γ Discount factor (difference in importance between future rewards and present rewards)
V(s') Value of the next state (s')

Calculation Steps:

    1. Identify the immediate reward (R): 10
    2. Identify the discount factor (γ): 0.9
    3. Identify the value of the next state (V): 20
    4. Apply the formula: V*(s) = R(s) + γ * V(s')
    5. Substitute the values: V*(s) = 10 + 0.9 * 20
    6. Calculate: V*(s) = 10 + 18 = 28

Calculation Examples

1. Basic Example:

Parameter Value
Reward (R) 10
Discount Factor (γ) 0.9
Next State Value (V) 20
Value Function (V*) 28

2. Advanced Example:

Parameter Value
Cumulative Reward (R) 50
Discount Factor (γ) 0.8
Next State Value (V) 30
Number of Steps (n) 5
Value Function (V*) 204


What is the discount factor (γ)?

The discount factor represents how much future rewards are valued compared to immediate rewards.

Can the calculator handle multiple steps?

Yes, the advanced calculator can compute values over multiple steps.

Is the calculator suitable for beginners?

Yes, it is designed to be user-friendly with both basic and advanced options.

Final Words

The Bellman Equation Calculator is a valuable tool for solving dynamic programming problems and understanding reinforcement learning. Try it out and share your experience with us. Your feedback helps us improve


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