Radiation Therapy Fractionation Calculator
Calculate BED and EQD2 from the Linear-Quadratic model for radiation therapy planning. Compare fractionation schedules and assess normal tissue toxicity.
About this calculator
Radiation oncologists compare fractionation schedules that deliver very different total physical doses using the Linear-Quadratic model, formalized by radiobiologist Jack Fowler in a landmark 1989 British Journal of Radiology review that remains the standard reference for BED and EQD2 in clinical practice, because a course of 30 fractions at 2 Gy each is not biologically equivalent to 5 fractions at 12 Gy each even though the physical totals are identical (both 60 Gy). Biologically Effective Dose (BED), computed as total dose times (1 plus dose-per-fraction divided by the tissue's alpha/beta ratio), converts any fractionation scheme into a common biological currency, and Equivalent Dose in 2 Gy fractions (EQD2) re-expresses that same BED as if it had been delivered in the conventional 2 Gy-per-fraction schedule most published dose tolerances are quoted against. The alpha/beta ratio is tissue-specific and is the reason the same physical dose can be "hotter" or "cooler" biologically depending on what it's hitting: most tumors and early-responding tissues use a ratio around 10 Gy, while late-responding normal tissues (the tissues where fibrosis, necrosis, and other delayed toxicities show up) use a lower ratio around 3 Gy, meaning they are more sensitive to large dose-per-fraction increases than the tumor-response calculation alone would suggest -- which is exactly why this calculator reports both a tumor BED and a separate late-normal-tissue BED side by side.
Total physical dose (fractions times dose per fraction) depends on nothing else in this calculator; neither the alpha/beta ratio nor the treatment schedule's days-per-week setting changes it, since those two inputs affect only the biological-equivalence and calendar-timing calculations layered on top of the same physical total. This tool computes BED and EQD2 only -- it does not model overall treatment time effects on tumor repopulation, incomplete repair between closely spaced fractions, or specific organ dose-volume constraints.
Medical Disclaimer
This calculator is for informational and educational purposes only. It is not a substitute for professional medical advice, diagnosis, or treatment. Always consult a qualified healthcare provider before making decisions about your health. Never disregard professional medical advice or delay seeking it because of results from this tool.
Inputs
Results
Total physical dose (Gy)
60
BED — Tumor (Gy)
72
Figures current as of 1989. Source: Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62(740):679-694.
How to Use This Calculator
- Enter the number of fractions and the dose per fraction (Gy) for the treatment course.
- Enter the tumor alpha/beta ratio (typical: 10 for most tumors, 1.5–4 for prostate cancer) and the number of treatments per week.
- Read the total physical dose (Gy), calculated as number of fractions × dose per fraction.
- Review the biologically effective dose (BED) and equivalent dose in 2 Gy fractions (EQD2) for both the tumor (your α/β) and late-responding normal tissue (α/β = 3), to compare fractionation schemes and assess toxicity risk.
- Check the estimated treatment duration in weeks and calendar days for the schedule.
How the result changes with Number of fractions
| Number of fractions | Total physical dose (Gy) | BED — Tumor (Gy) |
|---|---|---|
| 15 | 30 | 36 |
| 23 | 46 | 55.2 |
| 45 | 90 | 108 |
| 50 | 100 | 120 |
What each input means
- Number of fractions
- Total number of radiation fractions in the treatment course.
- Dose per fraction (Gy)
- Radiation dose delivered in each fraction.
- Tumor α/β ratio (Gy)
- α/β ratio for the target tissue. Typically 10 Gy for most tumors, 1.5–4 for prostate cancer, 3 for late-responding normal tissues.
- Treatments per week
- Number of treatment days per week (typically 5 for conventional, 3–5 for hypofractionation).
What each result means
- Total physical dose (Gy)
- Sum of all fraction doses: n × d.
- BED — Tumor (Gy)
- Biologically Effective Dose for tumor using the specified α/β ratio.
- EQD2 — Tumor (Gy)
- Equivalent dose in 2 Gy fractions for the tumor.
- BED — Late normal tissue (Gy₃)
- BED for late-responding normal tissue (α/β = 3 Gy). Higher values mean more toxicity risk.
- EQD2 — Late normal tissue (Gy)
- EQD2 for late-responding normal tissue.
- Treatment duration (weeks)
- Estimated treatment course length.
- Calendar days
- Total calendar days for the treatment course.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersNumber of fractions = 30, Dose per fraction (Gy) = 2, Tumor α/β ratio (Gy) = 10, Treatments per week = 5 = 4 input(s) provided
- Calculate Total physical doseTotal physical dose = numFractions * dosePerFraction60 = 60
- Calculate BED — TumorBED — Tumor = totalDose * (1 + dosePerFraction / alphaBetaRatio)72 = 72
- Calculate EQD2 — TumorEQD2 — Tumor = bed / (1 + 2 / alphaBetaRatio)60 = 60
- Calculate BED — Late normal tissueBED — Late normal tissue = totalDose * (1 + dosePerFraction / 3)100 = 100
Figures and sources
- Biologically Effective Dose (BED) — Linear-Quadratic radiobiology model (1989) — Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62(740):679-694.
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does total physical dose ignore the alpha/beta ratio entirely?
Total physical dose is simply the number of fractions times the dose per fraction -- a measurement of energy delivered, not of biological effect. The alpha/beta ratio only enters the calculation when converting that physical dose into BED or EQD2, which is why changing it moves those biological-equivalence outputs but leaves total physical dose completely unchanged.
Why does raising the alpha/beta ratio lower the calculated BED?
BED includes a term of dose-per-fraction divided by the alpha/beta ratio, so a larger ratio shrinks that fraction and pulls BED closer to the simple physical total. This mirrors the biology: tissues with a high alpha/beta ratio (around 10 Gy, typical of most tumors) are comparatively less sensitive to how the dose is split into fractions than tissues with a low ratio, like late-responding normal tissue around 3 Gy.
Why does this calculator show two separate BED values instead of one?
The tumor BED (using your entered alpha/beta ratio, typically around 10 Gy) and the late-responding normal tissue BED (fixed at an alpha/beta ratio of 3 Gy) answer different clinical questions -- tumor control versus long-term toxicity risk to nearby healthy tissue. A fractionation schedule can look favorable for tumor BED while still carrying meaningfully higher late-toxicity BED, which is exactly the tradeoff hypofractionated and SBRT regimens have to balance.
Does a shorter treatment course with fewer, larger fractions always mean a lower biological dose?
Not necessarily -- fewer fractions at a higher dose per fraction can produce a similar or even higher BED than a longer conventional course, because dose per fraction has an outsized effect on BED through the (1 + d/(alpha/beta)) term. This is exactly why hypofractionated and SBRT schedules require careful BED-based planning rather than simply comparing total physical dose or number of treatment days across schedules.
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