A concise, referenced explainer on equivalent dose, the linear-quadratic model, and retreatment
This page answers common questions about EQD2 (equivalent dose in 2 Gy fractions) and BED (biologically effective dose) for radiation oncology. It is an educational reference, not clinical guidance; the formulas, worked examples, and cited literature are provided for study and verification.
EQD2 is the equivalent dose in 2 Gy fractions: the total dose that, if delivered in 2 Gy fractions, would produce the same biological effect as a given schedule. It lets schedules with different fraction sizes be compared on a common scale. EQD2 is derived from the linear-quadratic model and depends on the tissue’s α/β ratio.1
EQD2 formula
EQD2 = D × (d + α/β) / (2 + α/β)
D = total dose · d = dose per fraction · α/β in Gy
BED is the biologically effective dose: a measure of the total biological effect of a fractionation schedule under the linear-quadratic model. BED is the dose that would produce a given effect in infinitely small fractions, and serves as the common currency from which EQD2 is derived.1,2
BED formula
BED = D × (1 + d / (α/β))
BED and EQD2 describe the same underlying biology in different units. BED expresses the total biological effect on an open-ended scale, useful for comparing the effect of widely different schedules. EQD2 re-expresses that effect as a familiar total dose in 2 Gy fractions, which clinicians read intuitively against conventional regimens. The two are related directly: EQD2 = BED / (1 + 2/(α/β)). A practical caution noted in the literature is that “biologically effective” (BED) and “biologically equivalent” (EQD2) are easily confused because the names are similar and both are reported in gray.2
The linear-quadratic (LQ) model describes the surviving fraction of cells after a radiation dose as the sum of a linear term (proportional to dose, governed by α) and a quadratic term (proportional to dose squared, governed by β). It is the most widely validated framework for relating total dose and dose per fraction to biological effect, and it underlies both BED and EQD2.1,3
The α/β ratio is the dose at which the linear and quadratic components of cell killing contribute equally. It captures a tissue’s sensitivity to fraction size: a low α/β means high sensitivity to large fractions. As a broad convention, tumours and early-responding tissues are modelled with a higher ratio of about 10 Gy, and late-responding normal tissues with a lower ratio of about 3 Gy.1 Prostate cancer is a notable exception, with evidence pointing to a low ratio near 1.5 Gy.4
Reported α/β values vary substantially within and between clinical studies; published estimates should be treated as ranges, not fixed constants.3
Take 20 Gy in 5 fractions (d = 4 Gy) for a late-responding tissue with α/β = 3 Gy:
Worked example — 20 Gy / 5 fx, α/β = 3
EQD2 = 20 × (4 + 3) / (2 + 3) = 20 × 7/5 = 28.0 Gy
BED = 20 × (1 + 4/3) = 46.7 Gy
A useful check: when the dose per fraction is exactly 2 Gy, EQD2 equals the total dose regardless of α/β (the identity case). For example, 60 Gy in 30 fractions gives EQD2 = 60.0 Gy for any α/β.
To combine radiation courses, convert each course to EQD2 separately and then sum the EQD2 values — using the same α/β for the tissue of interest. The physical doses (the “X Gy in Y fractions”) are never added directly, because identical physical doses can carry very different biological effects depending on fraction size. Summing biological dose is the only defensible way to estimate cumulative exposure across schedules.1
EQD2 Calculator enforces this rule: it converts each course independently and sums only the biological doses.
Summing EQD2 across courses implicitly assumes that none of the prior dose has been “forgiven” by tissue recovery. In reirradiation, some normal tissues may recover part of their tolerance between courses, but the magnitude is poorly characterized in humans and depends on the organ, the prior dose, and the interval. EQD2 Calculator offers an optional recovery correction that discounts a prior course’s contribution by a clinician-chosen percentage; it surfaces the assumption rather than resolving the biology.
The LQ model is best supported in the conventional range of roughly 1–8 Gy per fraction. At the very high doses per fraction used in stereotactic radiosurgery and SBRT, its applicability is debated: one view holds that the LQ model can overestimate cell kill and is inappropriate at such doses,5 while another argues it remains an acceptable method for determining isoeffective doses at large fraction sizes.6 Either way, EQD2 and BED estimates should be interpreted with extra caution outside the conventional fractionation range.
EQD2 Calculator is a free, browser-based tool intended for radiation oncologists, medical physicists, radiation therapists, and authorized researchers. It is an informational and educational aid — not a medical device and not a validated clinical treatment-planning system — and every output is meant to be independently verified. See the about page for how it works and the terms for full details.