BED / EQD2 Calculator

Put schedules with different doses per fraction on one scale using the linear-quadratic model. Enter each part of a treatment and the α/β your protocol specifies.

Educational SummaryAn original DoseLab explanation of a general concept. It teaches the idea; it is not a clinical recommendation.
Treatment

One row per part with its own dose per fraction (e.g. external beam, then a boost or brachytherapy).

Use the α/β your protocol specifies for the tissue and endpoint. Up to three values, separated by commas, to compare them side by side. α/β is always in Gy.

Worked examples

Results

Show the arithmetic

    Equivalent schedule

    The dose per fraction that gives the same total BED in another number of fractions, for each α/β.

    A schedule that matches one α/β does not match another. Use it to understand a schedule, not to convert a protocol's dose limits to a different fractionation unless that protocol tells you to.

    How it works

    BED = n × d × [1 + d ÷ (α/β)]
    EQD2 = BED ÷ [1 + 2 ÷ (α/β)] = n × d × (d + α/β) ÷ (2 + α/β)

    n is the number of fractions and d the dose per fraction. These are the formulas in Fowler's review of BED (2010). Each part of a treatment is converted separately and the results are added, which is only valid when every part uses the same α/β — so the calculator adds each α/β column on its own.

    BED is written with its α/β (72 Gy10, 100 Gy3). It is not an equivalent dose; EQD2 is the number to compare with a 2 Gy-per-fraction schedule. See BED and EQD2 for the explanation and examples.

    What this calculator does not do

    • No overall-time (repopulation) term. Fowler's full BED formula can subtract one; this calculator leaves it out, as DoseLab's BED page does.
    • No low-dose-rate or pulsed brachytherapy. Continuous or pulsed delivery needs a correction for repair during treatment (EMBRACE II, for example, assumes a repair half-time of 1.5 hours). Enter only fractionated, high-dose-rate or external-beam parts.
    • No α/β values of its own. Published tumor α/β values vary widely between and within sites (van Leeuwen 2018). Use your protocol's values and, where the choice is uncertain, compare a range.
    • No judgement on large fractions. Whether the LQ model holds at the large doses per fraction used in SBRT and SRS is debated (van Leeuwen 2018).
    • No dose limits. BED and EQD2 are modeling tools, not constraints. Your protocol's limits, institutional policy and physician directive take precedence.

    Sources

    Review articleSource Verified

    Review by the originator of the term biologically effective dose (BED, introduced in Br J Radiol in 1989). Gives the BED formula — nd[1 + d/(α/β)], with an optional overall-time term — and the conversion to the equivalent dose in 2 Gy fractions by dividing BED by 1 + 2/(α/β) (1.2 for α/β = 10 Gy, 1.67 for 3 Gy, 2.0 for 2 Gy). Its worked example: 30 × 2 Gy = 60 Gy is 72 Gy10 to early-responding tissue and 100 Gy3 to late-responding tissue, but 60 Gy EQD2 to both. Full text read in Europe PMC (PMC3473681).

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    Review articleSource Verified

    Systematic review of 64 clinical studies reporting α, β and α/β for human tumors. It found large heterogeneity within and between studies; estimates for prostate and breast tumors generally indicated high fractionation sensitivity, those for head & neck, cervix, bladder and liver tumors low sensitivity, and others were mixed. It notes that whether the LQ model holds at large fraction sizes is debated, and recommends choosing parameters by site, histology and model and exploring a range of values. Full text read in Europe PMC (PMC5956964).

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    Landmark trialSource Verified
    The EMBRACE II study: The outcome and prospect of two decades of evolution within the GEC-ESTRO GYN working group and the EMBRACE studies
    Pötter R, Tanderup K, Kirisits C, et al. · EMBRACE Collaborative Group / GEC-ESTRO GYN · 2018

    The overview of the EMBRACE II study of image-guided IMRT with chemotherapy followed by MRI-based adaptive brachytherapy for locally advanced cervical cancer. It sets out the study's external beam dose constraints (hard and soft, with separate bowel limits when the para-aortic nodes are treated), the brachytherapy planning aims and limits for the high-risk CTV, GTV, point A, bladder, rectum, sigmoid and bowel in total EQD2, and the vaginal dose points. Open access.

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    Clinical resourceSource Verified
    NRG Oncology Protocol Development Template for Radiation Therapy — Gynecological Cancer: Cervix, Uterine Cervix
    Lee YC, Benedict SH, Tsai P, Liang X, Padgett K, Portelance L · NRG Oncology Medical Physics Subcommittee / Radiation Oncology Committee · 2024

    The template NRG Oncology gives investigators for writing the radiation therapy section of a cervical cancer trial, covering external beam (photon, MR-linac and proton) and brachytherapy. It describes supine or prone setup, full- and empty-bladder simulation scans fused to build an internal target volume, diagnostic MRI and PET/CT fusion, standard structure names (including Spc_Bowel and BoneMarrow), example prescriptions, HDR point A and volume-directed (CTV_HR) brachytherapy, and per-protocol and variation-acceptable compliance criteria for both the external beam plan and the combined EBRT + brachytherapy dose. Its values are examples meant to be edited for each trial. DoseLab's cervix tables quote its per-protocol levels.

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