BED Calculator
Compute Biologically Effective Dose and Equivalent Dose in 2-Gy Fractions using the Linear-Quadratic model
The radiation dose delivered in each treatment session. Standard fractionation uses 1.8–2.0 Gy; hypofractionation uses 2.5–20 Gy per fraction.
The cumulative prescribed dose across all fractions. Equals dose per fraction multiplied by number of fractions.
The tissue-specific radiosensitivity ratio in Gy. Higher values indicate less sensitivity to fractionation changes. Select a preset or enter a custom value.
Acute delivery assumes instantaneous fraction delivery (standard external beam). Protracted delivery applies a dose rate correction factor for slow or continuous delivery such as brachytherapy.
Enter Parameters to Calculate BED
Input the dose per fraction, total dose, and alpha/beta ratio above. Results including BED, EQD2, charts, and clinical interpretation will appear here automatically.
Important
This calculator is provided for general information only and is not medical advice, diagnosis, or treatment. Results are estimates based on population averages and cannot account for your individual circumstances. Speak to a qualified healthcare professional before acting on anything you read here.
Compute Biologically Effective Dose and Equivalent Dose in 2-Gy Fractions using the Linear-Quadratic model
The Biologically Effective Dose (BED) calculator is an essential radiobiology tool used by radiation oncologists, medical physicists, and dosimetrists to quantify the true biological effect of a radiation treatment schedule. Unlike the simple physical dose measured in Gray (Gy), BED accounts for the fractionation pattern of radiation delivery and the intrinsic radiosensitivity of the irradiated tissue, providing a more meaningful measure of the therapeutic and toxic potential of a treatment plan. BED is derived from the Linear-Quadratic (LQ) model of cell killing, which is the most widely accepted mathematical framework in clinical radiobiology. The LQ model describes how ionizing radiation damages cells through two mechanisms: single-hit lethal events (the linear or alpha component) and cumulative sublethal damage that becomes lethal when two or more hits interact (the quadratic or beta component). The ratio of these two components, expressed as the alpha/beta ratio, characterizes the fractionation sensitivity of a given tissue type. Tissues with a high alpha/beta ratio, such as most tumors and early-responding normal tissues (alpha/beta approximately 10 Gy), are relatively insensitive to changes in fraction size. Tissues with a low alpha/beta ratio, such as late-responding normal tissues like the spinal cord, kidneys, and lung parenchyma (alpha/beta approximately 2 to 3 Gy), are highly sensitive to fraction size and are disproportionately affected by large doses per fraction. The standard BED formula for acute radiation delivery is BED = D multiplied by (1 + d divided by alpha/beta), where D is the total dose in Gray, d is the dose per fraction, and alpha/beta is the tissue-specific radiosensitivity ratio. For protracted or continuous low-dose-rate delivery, a dose rate correction factor g is introduced: BED = D multiplied by (1 + g times d divided by alpha/beta), where g ranges from 0 to 1 and accounts for the repair of sublethal damage that occurs during slow delivery. The related quantity EQD2 (Equivalent Dose in 2-Gy Fractions) converts any fractionation scheme to the biologically equivalent total dose that would be delivered using conventional 2-Gy fractions: EQD2 = D multiplied by (d + alpha/beta) divided by (2 + alpha/beta). EQD2 is particularly useful for comparing treatment plans that use different fraction sizes, as it normalizes everything to the familiar benchmark of 2 Gy per fraction. The clinical importance of BED and EQD2 has grown enormously over the past two decades as hypofractionation and stereotactic body radiation therapy (SBRT) have become mainstream treatment techniques. In conventional radiotherapy, typical fraction sizes range from 1.8 to 2.0 Gy, and BED values are relatively modest. In SBRT and stereotactic radiosurgery (SRS), fraction sizes can range from 6 to 20 Gy or more, producing dramatically higher BED values and correspondingly greater biological effects. Without BED calculations, it would be difficult to meaningfully compare a conventional 30-fraction treatment course with a 3-fraction SBRT regimen, even though both may deliver a similar level of tumor control. BED is also critical for evaluating cumulative radiation exposure when patients receive multiple courses of radiation therapy. For example, a patient who receives initial external beam radiation therapy followed by a brachytherapy boost will have BED contributions from both treatment phases. Because BED values are additive — BED total equals BED from course one plus BED from course two — clinicians can calculate the cumulative biological effect on both the tumor and nearby normal tissues. This is essential for staying within established normal tissue tolerance limits, particularly for organs at risk such as the spinal cord (typically limited to a cumulative BED of approximately 120 Gy with an alpha/beta of 2) or the rectum. This calculator implements all the standard radiobiological formulas and provides several advanced features not commonly found in competing tools. It supports both Gy and cGy input units with automatic conversion, predefined tissue-specific alpha/beta ratio presets, a protracted delivery mode with adjustable dose rate factor, a boost dose module for cumulative BED from multiple treatment courses, and a multi-schema comparison mode that allows side-by-side evaluation of up to five different fractionation schedules. Results include visual charts showing the breakdown of linear and quadratic components of BED, comparative bar charts across multiple alpha/beta ratios, and a comprehensive tissue reference table with published alpha/beta values for nine common tissue types. It is important to note that the LQ model has recognized limitations. It does not account for tumor repopulation during protracted treatment courses, which can significantly reduce the effective tumor BED for treatments lasting more than four to five weeks. The model's accuracy may also be reduced at very high doses per fraction (above approximately 6 to 8 Gy), although this remains debated in the radiobiology literature. Treatment breaks and gaps introduce additional complexity, with an estimated correction of approximately 1 Gy per day of interruption. Despite these limitations, BED remains the standard quantitative tool for comparing fractionation schemes in clinical radiation oncology and is recommended for use by major professional organizations including the American Association of Physicists in Medicine (AAPM) and the European Society for Radiotherapy and Oncology (ESTRO).
Understanding Biologically Effective Dose
BED quantifies the true biological impact of a radiation schedule by combining the physical dose with the fractionation pattern and tissue radiosensitivity. It is the standard metric for comparing radiation treatment regimens in modern oncology.
The Linear-Quadratic Model
The LQ model describes radiation cell killing through two mechanisms. The linear (alpha) component represents single-track lethal events where one radiation track causes an irreparable DNA double-strand break. The quadratic (beta) component represents the accumulation of two sublethal lesions from separate tracks that combine to become lethal. The alpha/beta ratio, expressed in Gy, is the dose at which the linear and quadratic contributions to cell killing are equal. This ratio determines how sensitive a tissue is to changes in fraction size. High alpha/beta tissues like most tumors show relatively little change in biological effect with different fractionation, while low alpha/beta tissues like spinal cord and kidney are profoundly affected by fraction size.
Alpha/Beta Ratios and Tissue Sensitivity
Different tissues have characteristic alpha/beta ratios that reflect their repair capacity and proliferative behavior. Early-responding tissues and most tumors have alpha/beta ratios of approximately 10 Gy, meaning they respond promptly to radiation and are less sensitive to fraction size. Late-responding normal tissues such as the spinal cord (2 Gy), kidneys (1.0 to 2.4 Gy), and connective tissue (3 Gy) have low alpha/beta ratios, making them highly sensitive to large fraction sizes. Prostate cancer is a notable exception among tumors, with an unusually low alpha/beta ratio of 1.1 to 1.5 Gy, which is why hypofractionated regimens are particularly effective for prostate cancer treatment.
BED vs. EQD2: When to Use Each
BED expresses the total biological effect of a treatment in absolute radiobiological terms. EQD2 converts that effect into the equivalent total dose delivered in standard 2-Gy fractions. In clinical practice, EQD2 is often preferred because it allows direct comparison with conventional fractionation regimens that most clinicians are familiar with. For example, a BED of 72 Gy (alpha/beta = 10) corresponds to an EQD2 of 60 Gy, which is immediately recognizable as a standard curative dose for many tumor types. BED is more useful when comparing across different tissue types or when performing cumulative dose calculations from multiple treatment courses.
Hypofractionation and SBRT Implications
Hypofractionation uses fewer fractions with higher doses per fraction than conventional radiotherapy. For tissues with low alpha/beta ratios, increasing the dose per fraction dramatically increases BED, which explains both the therapeutic advantage and the increased risk of late normal tissue toxicity. SBRT delivers very large fractions (typically 6 to 20 Gy per fraction in 1 to 5 treatments), producing BED values that can exceed 100 Gy even for high alpha/beta tumors. Clinicians must carefully evaluate BED for both tumor and critical normal structures when planning hypofractionated treatments. The therapeutic window exists because many tumors have higher alpha/beta ratios than the surrounding late-responding normal tissues.
BED Formulas
Biologically Effective Dose (BED)
BED = n × d × (1 + d / (α/β))
Where n = number of fractions, d = dose per fraction (Gy), and α/β = tissue-specific radiosensitivity ratio (Gy). Total dose D = n × d.
Equivalent Dose in 2-Gy Fractions (EQD2)
EQD2 = D × (d + α/β) / (2 + α/β)
Converts any fractionation scheme to the equivalent total dose delivered in standard 2 Gy fractions. Also expressed as EQD2 = BED / (1 + 2/(α/β)).
BED with Protracted Delivery
BED = D × (1 + g × d / (α/β))
Includes the dose rate factor g (0–1) for continuous or low-dose-rate delivery such as brachytherapy. Lower g means more sublethal repair during delivery.
Number of Fractions from Total Dose
n = D / d
Where D = total prescribed dose and d = dose per fraction. Both must be in the same units (Gy or cGy).
BED Reference Tables
Common α/β Ratios by Tissue Type
Published alpha/beta ratios for common tissues and tumors used in the Linear-Quadratic model. Higher values indicate less sensitivity to fractionation changes.
| Tissue / Tumor Type | α/β Ratio (Gy) | Fractionation Sensitivity |
|---|---|---|
| Early-responding tissues / most tumors | 10 | Low — relatively insensitive to fraction size |
| Late-responding normal tissues | 3 | High — strongly affected by fraction size |
| CNS (brain, spinal cord) | 2 | Very high — critical organ-at-risk |
| Kidneys | 1.0–2.4 | Very high — careful dose constraints required |
| Prostate cancer | 1.1–1.5 | Very high — favors hypofractionation |
| Head & neck tumors | 13.8–23 | Very low — conventional fractionation adequate |
| Breast | 3.5–4.6 | Moderate — hypofractionation increasingly standard |
| Cervix | 13 | Low — large fraction sensitivity comparable to tumors |
| Lung | 3–4.5 | Moderate to high — SBRT requires careful BED analysis |
Standard Fractionation Schemes and BED Values
Common radiation treatment prescriptions with their calculated BED and EQD2 values for α/β = 10 Gy (tumor) and α/β = 3 Gy (late tissue).
| Regimen | Total Dose | Fractions | BED (α/β=10) | BED (α/β=3) | EQD2 (α/β=10) |
|---|---|---|---|---|---|
| Conventional | 60 Gy | 30 × 2 Gy | 72.0 Gy | 100.0 Gy | 60.0 Gy |
| Moderate hypo | 55 Gy | 20 × 2.75 Gy | 70.1 Gy | 105.4 Gy | 58.4 Gy |
| Breast hypo (UK START) | 40.05 Gy | 15 × 2.67 Gy | 50.7 Gy | 75.7 Gy | 42.3 Gy |
| Prostate hypo | 60 Gy | 20 × 3 Gy | 78.0 Gy | 120.0 Gy | 65.0 Gy |
| Lung SBRT | 54 Gy | 3 × 18 Gy | 151.2 Gy | 378.0 Gy | 126.0 Gy |
| Brain SRS (single) | 20 Gy | 1 × 20 Gy | 60.0 Gy | 153.3 Gy | 50.0 Gy |
Worked Examples
Standard curative dose: 60 Gy in 30 fractions
A patient is prescribed 60 Gy in 30 fractions of 2 Gy each for a lung tumor. Calculate BED and EQD2 for both tumor tissue (α/β = 10 Gy) and late-responding normal tissue (α/β = 3 Gy).
Tumor BED (α/β = 10): BED = 60 × (1 + 2/10) = 60 × 1.2 = 72.0 Gy
Tumor EQD2 (α/β = 10): EQD2 = 60 × (2 + 10)/(2 + 10) = 60.0 Gy (equals total dose since d = 2 Gy)
Late tissue BED (α/β = 3): BED = 60 × (1 + 2/3) = 60 × 1.667 = 100.0 Gy
Late tissue EQD2 (α/β = 3): EQD2 = 60 × (2 + 3)/(2 + 3) = 60.0 Gy
Tumor BED = 72.0 Gy, Late tissue BED = 100.0 Gy. At 2 Gy/fraction, EQD2 equals the physical dose for all tissues. This is the conventional reference regimen.
Hypofractionated vs conventional for prostate cancer
Compare conventional prostate treatment (78 Gy in 39 fractions × 2 Gy) with hypofractionated (60 Gy in 20 fractions × 3 Gy). Prostate α/β = 1.5 Gy.
Conventional BED: 78 × (1 + 2/1.5) = 78 × 2.333 = 182.0 Gy
Hypofractionated BED: 60 × (1 + 3/1.5) = 60 × 3.0 = 180.0 Gy
Conventional EQD2: 78 × (2 + 1.5)/(2 + 1.5) = 78.0 Gy
Hypofractionated EQD2: 60 × (3 + 1.5)/(2 + 1.5) = 60 × 1.286 = 77.1 Gy
Both regimens have nearly identical BED for prostate (182.0 vs 180.0 Gy)
The hypofractionated regimen (60 Gy / 20 fx) achieves nearly the same tumor BED as conventional (78 Gy / 39 fx) because prostate cancer has a very low α/β ratio, making it ideal for hypofractionation.
Cumulative BED with external beam plus brachytherapy boost
A cervical cancer patient receives 50 Gy external beam (25 × 2 Gy) followed by a brachytherapy boost of 21 Gy (3 × 7 Gy). Calculate cumulative tumor BED (α/β = 10 Gy).
External beam BED: 50 × (1 + 2/10) = 50 × 1.2 = 60.0 Gy
Brachytherapy boost BED: 21 × (1 + 7/10) = 21 × 1.7 = 35.7 Gy
Cumulative BED: 60.0 + 35.7 = 95.7 Gy
Cumulative EQD2: 95.7 / (1 + 2/10) = 95.7 / 1.2 = 79.75 Gy
Combined tumor BED = 95.7 Gy (EQD2 ≈ 79.8 Gy). The brachytherapy boost adds significant biological dose due to the higher dose per fraction, enabling curative BED levels for cervical cancer.
How to Use the BED Calculator
Select Dose Unit and Enter Fraction Parameters
Choose your preferred dose unit — Gy (Gray) or cGy (centigray). Then enter the dose per fraction and total prescribed dose. The calculator automatically derives the number of fractions. For standard fractionation, typical values are 2.0 Gy per fraction with a total dose of 50 to 70 Gy. For SBRT, values might be 10 to 20 Gy per fraction with a total dose of 30 to 60 Gy.
Select the Alpha/Beta Ratio for Your Target Tissue
Choose a predefined tissue preset or enter a custom alpha/beta ratio. Use 10 Gy for most tumors and early-responding tissues, 3 Gy for late-responding normal tissues, 2 Gy for CNS and kidneys, or 1.5 Gy for prostate cancer. The alpha/beta reference table in the results panel provides published ranges for nine common tissue types to help you select the appropriate value.
Configure Delivery Mode and Optional Features
Select Acute for standard external beam delivery or Protracted for continuous low-dose-rate treatments like brachytherapy, then adjust the dose rate factor (g). Optionally, enable the Boost module to add a second treatment course and calculate cumulative BED, or enable Multi-Schema Comparison to evaluate up to five fractionation schedules side by side.
Review Results, Charts, and Export
The results panel displays BED, EQD2, fraction count, and alpha/beta ratio instantly. Review the BED component breakdown donut chart, the multi-ratio bar chart comparing BED across four standard alpha/beta values, and the clinical interpretation notes. Use the Export CSV button to download results for documentation or the Print button to generate a print-friendly version.
Frequently Asked Questions
What is BED and why is it used in radiation therapy?
Biologically Effective Dose (BED) is a radiobiological quantity that expresses the true biological impact of a radiation treatment schedule, accounting for both the total dose and the fractionation pattern. It is derived from the Linear-Quadratic model of cell killing. BED is essential because two treatment regimens delivering the same total physical dose can have very different biological effects depending on the dose per fraction. For example, 60 Gy in 30 fractions of 2 Gy has a different biological effect than 60 Gy in 20 fractions of 3 Gy. BED allows radiation oncologists to quantitatively compare these regimens and ensure that both tumor control probability and normal tissue complication probability are within acceptable limits.
What is EQD2 and how does it relate to BED?
EQD2, or Equivalent Dose in 2-Gy Fractions, converts any fractionation scheme into the total dose that would produce the same biological effect if delivered in standard 2 Gy fractions. It is calculated as EQD2 = D times (d + alpha/beta) divided by (2 + alpha/beta), or equivalently EQD2 = BED divided by (1 + 2/alpha/beta). EQD2 is widely preferred in clinical practice because most radiation oncologists have extensive experience with 2 Gy per fraction regimens and can intuitively interpret dose values in that context. When comparing a hypofractionated SBRT plan to a conventional plan, EQD2 provides a common reference frame.
How do I choose the correct alpha/beta ratio for my calculation?
The alpha/beta ratio depends on the tissue you are evaluating. For most tumors and early-responding normal tissues, use 10 Gy. For late-responding normal tissues such as connective tissue and muscle, use 3 Gy. For the central nervous system including brain and spinal cord, use 2 Gy. For kidneys, published values range from 1.0 to 2.4 Gy. Prostate cancer is a notable exception among tumors with an alpha/beta of approximately 1.1 to 1.5 Gy. Head and neck tumors have higher ratios of 13.8 to 23 Gy. When in doubt, use the reference table provided in this calculator and consult the radiation oncology literature for your specific clinical scenario.
What is the dose rate factor (g) and when should I use protracted delivery mode?
The dose rate factor g is a correction value between 0 and 1 that accounts for the repair of sublethal radiation damage during slow or continuous radiation delivery. In acute delivery mode (standard external beam), each fraction is delivered in minutes and g is effectively 1, meaning no significant repair occurs during irradiation. In protracted delivery, such as continuous low-dose-rate brachytherapy, repair occurs during delivery, reducing the quadratic component of cell killing. A g value of 0.5 means that half of the sublethal damage is repaired during delivery. Select protracted mode for brachytherapy or any scenario where the irradiation time per fraction is significantly longer than the sublethal damage repair half-time of the tissue.
How does the boost dose module work for cumulative BED?
The boost module allows you to add a second radiation treatment course, such as a brachytherapy boost following external beam therapy, or a sequential cone-down boost field. You enter the dose per fraction and total dose for the boost course, and the calculator computes its BED and EQD2 independently. The combined BED is the simple sum of the primary course BED and the boost course BED, which is a valid approach under the LQ model when both courses use the same alpha/beta ratio. This cumulative calculation is essential for ensuring that the total biological dose to critical structures such as the spinal cord, rectum, or bladder does not exceed established tolerance limits.
What are the limitations of the BED calculation?
The BED formula is based on the Linear-Quadratic model, which has several recognized limitations. First, it does not account for tumor cell repopulation during treatment, which can reduce effective tumor BED for protracted courses lasting more than four to five weeks. Second, its accuracy may be reduced at very high doses per fraction above approximately 6 to 8 Gy, though this is debated. Third, treatment breaks and gaps are not modeled, with an estimated correction of about 1 Gy per day of interruption needed. Fourth, the model assumes complete sublethal damage repair between fractions. Fifth, patient-specific biological variability in alpha/beta ratios is not captured by population-average values. Despite these limitations, BED remains the standard clinical tool for fractionation comparison.
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