How do I use this calculator?
Select a result mode, enter the other four quantities for one candidate point pair, and select Calculate.
Calculator Operations:
- Choose the result in Solve for, then enter the four known quantities. Use the same candidate pair for dose difference and spatial separation.
- Click Calculate to compute the selected result.
- Select Candidate gamma distance to evaluate one dose-and-distance pair.
- For an inverse, select the desired quantity and enter the candidate gamma distance plus the remaining known values.
Note: Full gamma is the minimum over candidate evaluation points. This tool evaluates one candidate pair without a spatial search. ฮD and ฮd must come from that same pair. A candidate above 1 does not establish full gamma failure; this educational tool cannot establish clinical treatment acceptance.
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.
Calculate a candidate gamma distance for one dose-and-distance point pair, or solve the fixed-pair equation for an input or criterion.
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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 evaluates the candidate point-pair distance ฮ. Dose difference and spatial separation must describe the same reference/evaluation pair. Full gamma is the minimum ฮ over a spatial search, which this tool does not perform.
Smaller candidate distances indicate closer agreement relative to the entered criteria. ฮ โค 1 identifies a qualifying candidate pair. ฮ > 1 for one pair cannot prove that full gamma fails, because another candidate may have a lower value.
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 | Candidate spatial separation 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 | This candidate pair lies inside the selected boundary; no full-distribution pass rate is calculated. |
| Equal to 1 | This candidate pair is on the mathematical boundary ฮ = 1. |
| Greater than 1 | This candidate pair is outside the boundary; full gamma may still be at or below 1 for another candidate. |
How to Calculate the Gamma Index
- Determine the dose difference, ΔD.
- Choose the dose criterion, ΔDcrit.
- Determine the spatial separation, Δd, for the same candidate pair as the dose difference.
- Choose the distance criterion, Δdcrit.
- Choose Candidate gamma distance, enter the four quantities with consistent dose basis and distance units, and select Calculate.
- Interpret the candidate distance relative to 1; do not infer a full gamma failure or clinical treatment acceptance.
Rearranged Forms
Because the calculator can solve for any one missing value, the gamma equation can be rearranged as needed.
Solve for dose difference
Solve for candidate spatial separation
Solve for dose criterion
Solve for distance criterion
Difference/separation inverses require a nonnegative radicand; the dose inverse returns magnitude, with signs ยฑ possible. Criterion inverses require a positive denominator and numerator magnitude. A zero denominator may mean no finite solution or a nonunique positive criterion. Both criteria must be positive.
Example Calculation
If the dose difference is 0.5, the dose criterion is 1.0, the candidate spatial separation is 2.0, and the distance criterion is 5.0, then:
The candidate distance is approximately 0.64031242. This candidate pair lies within the selected boundary; it does not establish a full-distribution pass rate or treatment acceptance.
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.
