BED Calculator - Biologically Effective Dose and EQD2
This BED calculator uses the linear-quadratic (LQ) model to work out the Biologically Effective Dose and the Equivalent Dose in 2-Gy fractions (EQD2) for any radiotherapy fractionation schedule. Enter the dose per fraction, the number of fractions, and either choose a tissue type preset or type in a custom alpha/beta ratio. Results update instantly and a comparison chart lets you visualise how altering the fractionation changes the BED and EQD2.
What is BED (Biologically Effective Dose)?
The Biologically Effective Dose is a radiobiological quantity that represents the total biological effect a given fractionation schedule has on a tissue, expressed in Gray (Gy). Unlike physical dose, BED accounts for the fact that the same total dose delivered in different numbers of fractions has very different biological consequences. Larger doses per fraction cause proportionately more cell kill, particularly in tissues with a low alpha/beta ratio such as late-reacting normal tissues. The linear-quadratic (LQ) model underpins BED calculations and has been validated for conventional fractionation and moderate hypofractionation. Its use for extreme hypofractionation (SBRT/SABR, doses above 5-6 Gy per fraction) is more controversial and should be interpreted with caution.
How BED and EQD2 are calculated
The BED formula is: BED = n x d x (1 + d / (alpha/beta)), where n is the number of fractions and d is the dose per fraction in Gray. The term in brackets is the Relative Effectiveness (RE) factor for each fraction. The alpha/beta ratio characterises the tissue: late-reacting normal tissues have low values (typically 2-3 Gy), meaning they are more sensitive to changes in fraction size; tumors and early-reacting tissues usually have higher values (8-13 Gy). EQD2 (Equivalent Dose in 2-Gy fractions) converts BED back into a dose figure that is directly comparable between regimens. It is calculated as: EQD2 = BED / (1 + 2 / (alpha/beta)). A BED of 72 Gy for a late tissue (alpha/beta = 3) corresponds to an EQD2 of 60 Gy, which is the conventional 2-Gy-per-fraction dose that produces the same late effect.
The alpha/beta ratio and tissue sensitivity
The alpha/beta ratio is the cornerstone of the LQ model. It reflects the balance between two types of radiation-induced cell damage: the linear (alpha) component, proportional to dose, represents lethal single-track events; the quadratic (beta) component, proportional to dose squared, represents repairable double-strand breaks that can accumulate between fractions. Tissues with a low alpha/beta ratio (2-3 Gy), such as the spinal cord, kidney, and late-responding lung, are more sensitive to high doses per fraction. This is why hypofractionated schedules require careful dose constraints for these organs at risk. Prostate cancer is notable for having a low alpha/beta ratio (around 1.5-3 Gy), similar to late normal tissues, which actually makes it a good candidate for hypofractionation because the tumor receives a higher BED without proportionately increasing toxicity.
Clinical applications: standard, hypo-, and hyperfractionation
Conventional fractionation uses 1.8-2 Gy per fraction, typically 5 days per week. Hypofractionation (larger fractions, fewer sessions) is now standard for breast, prostate, and lung (SBRT) cancers: it is more convenient for patients and, for tumors with low alpha/beta ratios, it can be biologically equivalent or superior. Extreme hypofractionation such as SBRT (5-20 Gy per fraction in 1-5 sessions) achieves very high BED values. For example, 60 Gy in 3 fractions of 20 Gy gives a BED of 60 x (1 + 20/10) = 180 Gy for a tumor with alpha/beta = 10. Hyperfractionation uses smaller doses per fraction delivered twice daily to reduce late effects while maintaining tumor control. The BED and EQD2 calculated here allow direct comparison across all these regimens for any tissue endpoint.
Common tissue alpha/beta ratios
| Tissue / endpoint | Alpha/beta ratio (Gy) | Type | Clinical relevance |
|---|---|---|---|
| Spinal cord | 2 | Late-reacting | Dose-limiting in spinal, para-spinal tumors |
| Brainstem | 2 | Late-reacting | Dose-limiting in posterior fossa RT |
| Kidney | 2 | Late-reacting | Relevant in abdominal RT |
| Brachial plexus | 2.5 | Late-reacting | Relevant in axillary/supraclavicular fields |
| Breast | 3.5 | Late-reacting | Supports hypofractionation protocols |
| Prostate tumor | 3 | Tumor | Justifies moderate/extreme hypofractionation |
| Late-reacting tissue (general) | 3 | Late-reacting | Default for normal tissue tolerance |
| Lung | 3.5 | Late-reacting | Pneumonitis risk planning |
| Bowel | 4 | Late-reacting | Abdominal and pelvic RT planning |
| Bladder | 5 | Late-reacting | Relevant in pelvic RT |
| Early-reacting tissue (general) | 10 | Early-reacting | Mucositis, skin reactions |
| Tumor (general) | 10 | Tumor | Standard assumption for most solid tumors |
| Head and neck tumor | 13 | Tumor | Altered fractionation trials |
Consensus values used in clinical radiobiology. Range reflects variability across published studies. Select a preset in the calculator to use the mid-point value.
Frequently asked questions
What does BED mean in radiation therapy?
BED stands for Biologically Effective Dose. It is a way of expressing the total biological effect of a radiotherapy schedule on a tissue, regardless of how many fractions were used or how large each fraction was. Because larger fractions cause disproportionately more damage (especially to late-reacting normal tissues), the physical dose alone does not tell you the full biological impact. BED adds a correction factor based on the dose per fraction and the tissue sensitivity (alpha/beta ratio), giving a single number that can be compared across different regimens.
What is the difference between BED and EQD2?
BED is a theoretical quantity representing the total biological effect. EQD2 converts that value back into a clinically familiar dose: the dose in standard 2-Gy fractions that would produce exactly the same biological effect. EQD2 is useful because oncologists know from decades of data how specific normal tissues respond to 2-Gy-per-fraction schedules. By expressing any regimen as EQD2, you can directly compare it with published dose constraints and historical data. For example, a spinal cord EQD2 of 45 Gy (alpha/beta = 2) corresponds to the conventionally accepted tolerance limit for that structure.
What alpha/beta ratio should I use?
The alpha/beta ratio should match the tissue or endpoint you are calculating for. For late-reacting normal tissues (the most common clinical concern for toxicity), use 2-3 Gy. For most solid tumors and early-reacting tissues (skin, mucosa), use 10 Gy. Prostate cancer is an important exception: its alpha/beta ratio is estimated at about 1.5-3 Gy, closer to late normal tissue, which is one reason hypofractionated prostate radiotherapy is effective. Head and neck tumors have a higher alpha/beta around 13 Gy. When in doubt, consult your institution protocol or the original clinical trial data for the regimen you are comparing.
Does BED apply to SBRT and SABR?
The LQ model was developed and validated for conventional fractionation (1.8-2 Gy per fraction). Its accuracy at the high doses per fraction used in SBRT (5-20+ Gy) is debated. Some evidence suggests the LQ model overestimates cell kill at very high doses per fraction, meaning true BED may be slightly lower than the formula predicts. Modified models such as the linear-quadratic-linear (LQL) model attempt to correct for this, but they require additional parameters and are less widely adopted. SBRT BED values calculated here should be interpreted as approximations that are useful for comparison purposes but carry greater uncertainty than those for conventional fractionation.
Can I use this calculator to compare two treatment plans?
Yes. Run the calculator for each regimen using the same tissue preset or alpha/beta ratio, and compare the resulting BED and EQD2 values. Two schedules with the same EQD2 for a given tissue are predicted by the LQ model to produce the same biological effect in that tissue. The chart in this calculator shows how BED and EQD2 change as the number of fractions varies while the total physical dose stays constant, which illustrates why more fractions with a lower dose per fraction reduces the BED for late-reacting tissues.
Why is a high alpha/beta ratio better for tumors?
A high alpha/beta ratio means the tissue is relatively insensitive to changes in fraction size: the biological effect scales almost linearly with total dose regardless of fraction size. This is true for most tumors and early-reacting tissues (mucosa, skin). A low alpha/beta ratio, by contrast, means the tissue is very sensitive to fraction size: doubling the dose per fraction has more than double the biological effect per unit of physical dose. When a tumor has a low alpha/beta ratio (like prostate cancer), hypofractionation kills it disproportionately more, which is the biological rationale for extreme hypofractionation in that disease.
Sources
- Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol. 1989;62(740):679-694.
- Joiner MC, van der Kogel A (eds). Basic Clinical Radiobiology, 4th edition. CRC Press, 2009. Chapter 8: Fractionation: the linear-quadratic approach.
- Dale RG. The application of the linear-quadratic dose-effect equation to fractionated and protracted radiotherapy. Br J Radiol. 1985;58(690):515-528.