Enter the difference in dose values, reference dose value, difference in distance values, and maximum distance value into the calculator to determine the Gamma Index.

Gamma Index Formula

The following formula is used to calculate the Gamma Index.

GI = sqrt((ΔD/D_ref)^2 + (Δd/d_max)^2)


  • GI is the Gamma Index
  • ΔD is the difference in dose values
  • D_ref is the reference dose value
  • Δd is the difference in distance values
  • d_max is the maximum distance value

To calculate the Gamma Index, square the ratio of the difference in dose values to the reference dose value. Add this to the square of the ratio of the difference in distance values to the maximum distance value. The Gamma Index is the square root of this sum.

What is a Gamma Index?

A Gamma Index is a quantitative tool used in radiation therapy to compare the differences between measured and calculated dose distributions. It combines both the dose difference and distance-to-agreement criteria into a single metric, providing a comprehensive evaluation of the accuracy of treatment plans. A lower Gamma Index indicates a closer match between the measured and calculated dose distributions, suggesting a higher accuracy of the treatment plan.

How to Calculate Gamma Index?

The following steps outline how to calculate the Gamma Index for a given problem.

  1. First, determine the difference in dose values (ΔD).
  2. Next, determine the reference dose value (D_ref).
  3. Next, determine the difference in distance values (Δd).
  4. Finally, determine the maximum distance value (d_max).
  5. Using the formula GI = sqrt((ΔD/D_ref)^2 + (Δd/d_max)^2), calculate the Gamma Index.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

ΔD: difference in dose values = 0.5

D_ref: reference dose value = 1.0

Δd: difference in distance values = 2.0

d_max: maximum distance value = 5.0