How do I use this calculator?
This calculator allows you to calculate any one of the variables shown directly above by entering the other four values.
Calculator Operations:
- Fill in any four of the five fields (ฮD, ฮDcrit, ฮd, ฮdcrit, GI) and leave the value you want to solve for blank.
- Click Calculate to compute the missing value.
- To calculate the gamma value (GI), leave GI blank and enter the other four values.
- To calculate a different variable, enter a gamma value (GI) and leave that variable blank. (The GI field is editable.)
Note: Full radiotherapy gamma analysis is defined point-by-point using a spatial search/minimization over nearby comparison points in a dose distribution. This calculator uses the simplified โfixed-pointโ form (no spatial search), which is appropriate when ฮD and ฮd are already taken with respect to the relevant comparison point and criteria.
Use the calculate button when all known values have been entered and use the reset button when you want to clear the values from the calculator.
Enter the dose difference (ฮD), the dose-difference criterion (ฮDcrit), the distance-to-agreement (ฮd), and the distance criterion (ฮdcrit) into the calculator to determine the (fixed-point) gamma value (GI). Use consistent units (ฮD and ฮDcrit in the same dose units; ฮd and ฮdcrit in the same distance units).
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Gamma Index Formula
The gamma index (GI) is a dimensionless radiotherapy quality-assurance metric that combines dose error and spatial error into a single result. This calculator uses the fixed-point form of gamma, which is appropriate when the dose difference and distance-to-agreement have already been identified for the comparison being evaluated.
GI = \sqrt{\left(\frac{\Delta D}{\Delta D_{crit}}\right)^2 + \left(\frac{\Delta d}{\Delta d_{crit}}\right)^2}In practical terms, smaller gamma values indicate better agreement. A gamma value at or below 1 means the point satisfies the selected tolerance criteria.
GI \le 1
Variable Definitions
| Variable | Description | Unit Notes |
|---|---|---|
| GI | Gamma index value | Unitless |
| ΔD | Dose difference between the compared values | Use the same dose basis as ΔDcrit |
| ΔDcrit | Allowed dose-difference criterion or tolerance | Must be positive and in the same dose units as ΔD |
| Δd | Distance-to-agreement for the comparison | Use the same distance units as Δdcrit |
| Δdcrit | Allowed distance criterion or tolerance | Must be positive and in the same distance units as Δd |
How to Interpret Gamma Index
| Gamma Result | Interpretation |
|---|---|
| Less than 1 | The comparison passes with margin to spare. |
| Equal to 1 | The comparison is exactly on the acceptance boundary. |
| Greater than 1 | The comparison fails the selected criteria. |
How to Calculate the Gamma Index
- Determine the dose difference, ΔD.
- Choose the dose criterion, ΔDcrit.
- Determine the distance-to-agreement, Δd.
- Choose the distance criterion, Δdcrit.
- Substitute the values into the formula.
- Interpret the result relative to the pass threshold of 1.
Rearranged Forms
Because the calculator can solve for any one missing value, the gamma equation can be rearranged as needed.
Solve for dose difference
\Delta D = \Delta D_{crit}\sqrt{GI^2 - \left(\frac{\Delta d}{\Delta d_{crit}}\right)^2}Solve for distance-to-agreement
\Delta d = \Delta d_{crit}\sqrt{GI^2 - \left(\frac{\Delta D}{\Delta D_{crit}}\right)^2}Solve for dose criterion
\Delta D_{crit} = \frac{\Delta D}{\sqrt{GI^2 - \left(\frac{\Delta d}{\Delta d_{crit}}\right)^2}}Solve for distance criterion
\Delta d_{crit} = \frac{\Delta d}{\sqrt{GI^2 - \left(\frac{\Delta D}{\Delta D_{crit}}\right)^2}}For these rearranged forms to produce a real-valued result, the quantity inside the square root must be zero or greater, and both criteria must be greater than zero.
Example Calculation
If the dose difference is 0.5, the dose criterion is 1.0, the distance-to-agreement is 2.0, and the distance criterion is 5.0, then:
GI = \sqrt{\left(\frac{0.5}{1.0}\right)^2 + \left(\frac{2.0}{5.0}\right)^2}GI = \sqrt{0.25 + 0.16} = \sqrt{0.41} \approx 0.64Since 0.64 is less than 1, the point meets the chosen criteria.
Important Usage Notes
- Keep dose units consistent between ΔD and ΔDcrit.
- Keep distance units consistent between Δd and Δdcrit.
- Do not use zero for either criterion; both tolerances must be positive.
- If dose criteria are based on percent, make sure the percent basis is applied consistently before calculating.
- This simplified calculator does not perform the spatial search used in full distribution-based gamma analysis; it evaluates the fixed-point form once the comparison quantities are already known.
Common Questions
- Is the gamma index a percentage?
- No. The gamma index is unitless. It is built from normalized dose and distance terms.
- What does a lower gamma value mean?
- A lower value means the measured and reference results agree more closely relative to the chosen tolerances.
- Can I mix dose units?
- No. If ΔD is entered in cGy, then ΔDcrit must also be in cGy. The same consistency rule applies to distance units.
- Why can the calculator solve for any variable?
- The gamma relationship is algebraic in this fixed-point form, so the equation can be rearranged to isolate any one unknown when the other four values are known.
