Radiation Oncology · Calculator

BED, EQD2, Re-irradiation and Treatment Gap Calculator

Schedule comparison and isoeffective conversion, cumulative re-irradiation dose, common schedules, and compensation for missed treatment days

  • Updated November 2026

Four tools for fractionated treatment: how two schedules compare at any α/β, how much room a previously irradiated structure has left, where common radiosurgery and CNS schedules sit in BED and EQD2, and how to compensate when treatment days are missed. Each tool states its model and its sources. Built for teaching and discussion. For patient care, use the approved treatment plan and your team's dose constraints.

Timoteo Almeida, MD, MSc, PhD, FCNS  |  Departments of Neurological Surgery and Radiation Oncology

About the model, units and related pages

Orientation

All four tools use the linear-quadratic (LQ) model, which is least reliable at single-fraction radiosurgery doses (a point still debated: Kirkpatrick and colleagues argue against its use there, Brenner for it); the treatment gap tool adds a term for tumor repopulation over time. Use the numbers to compare schedules and to check reasoning, not to set a dose. Radiosurgery BED with treatment time, dose falloff and normal tissue risk are on the Radiosurgery Dose Calculator; trial schedules and normal-tissue limits are on the Dose Tables page; and the biology of high dose per fraction is on Radiobiology. Dose units are Gy; volumes are cc (cm³); fx = fractions.

Part I

BED and EQD2

1.Schedule comparison

BED = n · d · (1 + d / [α/β]); EQD2 = BED / (1 + 2 / [α/β]) (Fowler 1989). Enter any α/β or pick a preset (sources in section 2). The comparison line shows the same schedule at α/β 10 and 2, the usual tumor and late-CNS values, so the trade between tumor effect and normal-tissue cost is visible at a glance. At single-fraction doses, the LQ model is the convention HyTEC uses; LQ-L is shown as the alternative.

Total dose
27.0 Gy
BED
51.3 Gy
EQD2
42.8 Gy

α/β 10: BED 51.3, EQD2 42.8 Gy · α/β 2: BED 148.5, EQD2 74.3 Gy

Isoeffective conversion

-

2.Which α/β to use

For late CNS effects, α/β = 2 is a defensible default: both HyTEC radiosurgery papers that cover the brain and the spinal cord used it, and 76% of respondents in an international CNS re-irradiation survey (Chen 2025) use it for organs at risk. At 1–5 fractions, doubt about whether the LQ model holds at all matters more than the choice between 2 and 3. The values below are model conventions, not measured constants; when comparing with a published table, use the α/β that table was built on.

Conventional α/β values and their sources. Ranges show how widely published estimates vary.
TissuePresetRangeBasisSource
Brain (radionecrosis)22–3HyTEC converted multifraction SRS with 2; QUANTEC used 3 for conventionally fractionated dataMilano 2021 (HyTEC brain); Lawrence 2010 (QUANTEC)
Brainstem22.1–3.3QUANTEC drew dose-response curves at 2.1, 2.5, and 3.3; no dedicated HyTEC brainstem modelMayo 2010 (QUANTEC)
Optic nerve and chiasm1.61.6–2HyTEC used 1.6 from Jiang 1994; at 2, its 1-fraction 1% risk dose falls from 12.1 to 11.4 Gy. Most re-irradiation limits use 2 or 2.5Milano 2021 (HyTEC optic); Jiang 1994
Spinal cord, cervical and thoracic2about 1–2.7HyTEC thecal-sac limits are EQD2 at 2; QUANTEC’s human estimate was lowerSahgal 2021 (HyTEC cord); Kirkpatrick 2010 (QUANTEC)
Lumbar cord, cauda equina42–4Used by Nieder for re-irradiation bookkeeping; low confidenceNieder 2005
Brain metastasis, glioma1010–12Conventional tumor value; glioma estimates are very impreciseConvention
Meningioma3.32.7–4.6Derived from single-fraction and fractionated isoeffective dosesShrieve 2004; Vernimmen 2010
Vestibular schwannoma2.4about 1–4Fractionation-effect analysis of published seriesVernimmen 2010
Arteriovenous malformation2.2contestedFitted to obliteration rates (2.2 ± 1.6); other methods give very different valuesQi 2007; Vernimmen 2010
Part II

Re-irradiation

3.Cumulative dose to a structure

This tool follows the usual planning sequence. Enter the dose the structure already received (tick the box below the first course if there were more), read from the dose-volume histogram at the same point or volume (for example, point maximum or D0.1cc); use the prior prescription only when the structure sat inside the prior target. Choose a cumulative EQD2 goal and, if the goal allows it, a forgiveness percentage. The tool returns the EQD2 left, checks a planned course against the goal with the risk the published data support, and shows the remaining budget as a dose per fraction for 1 to 30 fractions. Add up to three more structures and each row is set by the structure with the least room left.

Set to the value the chosen limit was built on.

Prior course, dose to the structure

Cumulative goal and forgiveness

Planned course (optional)

    4.How cumulative limits are used in practice

    The workflow most centers describe has five steps: retrieve the prior plan and map its dose onto the new planning scan (rigid or deformable registration); convert both courses to EQD2 with an α/β for each organ; forgive part of the prior course (a recovery discount) if the center does so; subtract from a cumulative limit to get the remaining budget; and choose the fractionation that fits. The Michigan physics consult published a worked example of exactly this arithmetic, and the ESTRO-EORTC consensus asks that equieffective doses be used for any summation, that maximum doses be used for serial organs such as the cord, and that the α/β and recovery assumptions be reported.

    Practice varies widely. In an international survey of CNS re-irradiation (Chen 2025), 88% of respondents evaluated cumulative equieffective dose and 76% used α/β = 2 for organs at risk, with no consensus on tolerances; in a 17-center survey (Stroom 2025), cumulative limits ran a median 26% above first-course limits, mostly through a median recovery factor of 23%. ESTRO-EORTC (Andratschke 2022) judged recovery discounts too uncertain to recommend in general, “except for central nervous system and spinal cord,” where primate data (Ang 2001) show substantial cord recovery: after 44 Gy, an estimated 76%, 85%, and 101% of the initial dose was recovered at 1, 2, and 3 years.

    Forgiveness or a raised limit, not both Published limits handle recovery in one of two ways. Some keep a near-first-course limit and forgive part of the prior dose (the Michigan template: 0% under 3 months, 10% at 3–6 months, 25% at 6–12 months, 50% at 1 year or more). Others apply no discount and set a higher cumulative limit instead (Nieder, Sahgal, the nasopharyngeal carcinoma consensus, the ReCOG glioma review). Applying forgiveness on top of a raised limit counts the same recovery twice, so the calculator does not apply forgiveness to a limit built without it unless you tick “Apply forgiveness anyway”; it then flags the double count and judges risk on the uncredited sum.

    5.Published cumulative levels in the CNS

    Cumulative EQD2 at α/β = 2 unless stated (the nasopharyngeal consensus did not specify α/β; 2 is assumed, and its levels equal 130% and 150% of standard first-course limits). None is validated for every situation; institutional templates are shown as published and were not endorsed by their authors for use elsewhere.
    StructureCumulative levelForgivenessContextSource
    BrainAbout 100 GyNo forgivenessNecrosis above this level after conventional re-irradiation of glioma; fractionated stereotactic series 90–133.9 Gy and SRS 111.6–137.2 Gy without more necrosis, linked by the authors to smaller volumes; interval did not predict necrosisMayer and Sminia 2008; Sminia and Mayer 2012
    Brain100–110 GyNo forgivenessCandidate limit for recurrent glioblastoma; none of 27 studies used recovery factorsSlevin 2026 (ReCOG review)
    Temporal lobe91 Gy desirable, 105 Gy acceptable (D0.03cc)No forgivenessNasopharyngeal carcinoma consensusNg 2021, as tabulated by Beddok 2025
    Brain, brainstem (children)Median prescription 103.8 GyNo forgivenessPediatric re-irradiation, 449 patients: brain necrosis 4.9%, brainstem necrosis 3.1%Ajithkumar 2024 (PENTEC)
    Brainstem85–100 Gy (max)No forgivenessCandidate limit for recurrent glioblastoma, < 5% severe toxicitySlevin 2026
    Brainstem70.2 Gy desirable, 81 Gy acceptable (D0.03cc)No forgivenessNasopharyngeal carcinoma re-irradiation consensusNg 2021, as tabulated by Beddok 2025
    Brainstem64 Gy (D0.1cc, α/β 2.5)Forgiveness by intervalMichigan physics consult templateParadis 2019
    Optic apparatus75–80 Gy (max)No forgivenessCandidate limit for recurrent glioblastomaSlevin 2026
    Optic apparatus70.2 Gy desirable, 81 Gy acceptable (D0.03cc)No forgivenessNasopharyngeal carcinoma consensusNg 2021, as tabulated by Beddok 2025
    Optic apparatus54 Gy (D0.1cc, α/β 2.5)Forgiveness by intervalMichigan templateParadis 2019
    Spinal cord, conventional60 Gy (BED 120 Gy2) to 67.8 Gy (BED 135.5 Gy2)No forgivenessNo myelopathy reported up to 60 Gy, small risk up to 67.8 Gy, when each course is ≤ 49 Gy and the interval ≥ 6 months; α/β 4 was used for the lumbar cordNieder 2005, 2006
    Spinal cord, conventional58.5 Gy desirable, 67.5 Gy acceptable (D0.03cc)No forgivenessNasopharyngeal carcinoma consensusNg 2021, as tabulated by Beddok 2025
    Spinal cord, conventional50 Gy (D0.1cc; 55 Gy within 2 mm of target; α/β 2.5)Forgiveness by intervalMichigan templateParadis 2019
    Cauda equina60 Gy (D0.1cc, α/β 2.5)Forgiveness by intervalMichigan template; Nieder used α/β 4 for the lumbar cord against the BED levels aboveParadis 2019; Nieder 2005
    Spinal cord, SBRT re-irradiationAbout 70 Gy (thecal sac point max)No forgivenessSBRT course 20–25 Gy and no more than about half the total, ≥ 5 months after conventional palliative RTSahgal 2012
    Nieder myelopathy risk score for conventional spinal cord re-irradiation (BED at α/β = 2; Nieder used 4 for the lumbar cord). The planned-course alert uses this score for the spinal cord and cauda equina. Score table as reproduced by Rades 2024.
    FactorPoints
    Interval between courses under 6 months4.5
    Either course BED ≥ 102 Gy24.5
    Cumulative BED ≤ 120 Gy20
    Cumulative BED, each 10 Gy2 band above 120 (120.1–130 = 1 … > 200 = 9)1 to 9
    Risk group (2005 series, 40 patients)0–3 points low (0 of 24 with myelopathy); 4–6 intermediate (2 of 6); > 6 high (9 of 10)
    Risk group (2006 update)Myelopathy in 3% low, 25% intermediate and 90% high
    Before summing doses Summed EQD2 assumes the two courses hit the same tissue at the same point, which is rarely exact after deformation, resection, or a different technique; assuming the high-dose regions overlap is the conservative default. Above about 10 Gy per fraction the LQ model may overstate the effect (cell-survival curves straighten at high dose), although vascular and immune effects proposed by Kirkpatrick and colleagues could act the other way. Use deformable registration of the prior plan when it is available, and have physics review any re-irradiation sum.
    Part III

    Common Schedules

    6.Common schedules in BED10 and EQD2

    Tumor effect (α/β = 10) beside late-CNS cost (α/β = 2). Single fractions above about 10 Gy are shown at α/β = 2 for comparison only; the LQ model may overstate their effect, although some argue the opposite. Tap a schedule to load it into the calculator in Part I.
    ScheduleTypical useBED10EQD210EQD22
    24 Gy × 1Intact metastasis < 1 cm (A071801); RTOG 90-05 ceiling ≤ 2 cm81.668.0156.0
    22 Gy × 1Intact metastasis 1–2 cm (A071801)70.458.7132.0
    20 Gy × 1Smallest cavity tier (< 4.2 cc), N107C and A07180160.050.0110.0
    18 Gy × 1Intact metastasis 2–3 cm (RTOG 90-05)50.442.090.0
    17 Gy × 1Cavity 8.0–14.3 cc (N107C, A071801)45.938.380.8
    15 Gy × 1Intact metastasis 3–4 cm (RTOG 90-05)37.531.363.8
    14 Gy × 1Cavity 20.0–29.9 cc (N107C, A071801)33.628.056.0
    12 Gy × 1Largest cavity tier (≥ 30 cc), N107C and A07180126.422.042.0
    27 Gy / 3Cavity < 30 cc (A071801); large intact metastasis51.342.874.3
    24 Gy / 3Large intact metastasis, institutional series43.236.060.0
    30 Gy / 5Cavity ≥ 30 cc (A071801); large intact metastasis48.040.060.0
    25 Gy / 5Perioptic or brainstem-adjacent targets, institutional series37.531.343.8
    24 Gy / 2Spine SBRT (CCTG SC.24)52.844.084.0
    16 Gy × 1Spine SRS (RTOG 0631, 16 or 18 Gy)41.634.772.0
    8 Gy × 1Palliative spine or bone (RTOG 0631 comparator)14.412.020.0
    30 Gy / 10Whole-brain RT, including hippocampal avoidance39.032.537.5
    25 Gy / 10Prophylactic cranial irradiation31.326.028.1
    Part IV

    Treatment Gap

    7.Compensating for missed treatment days

    When unscheduled interruptions lengthen a course, tumors that repopulate quickly can lose effective dose. The Royal College of Radiologists guidance (RCR 2019) names transfer to a matched machine on the day of the interruption as the ideal. After that, the ways to compensate, in order of preference, are: treat on weekend or bank-holiday days, treat twice a day at least 6 hours apart, give fewer, larger fractions to finish on the planned day, and, when the course has to be extended, keep the extension as short as possible with an adjusted dose; keeping the delayed schedule and adding dose comes last (the order follows a modelled comparison of the methods, Hendry 1996). The tool counts the days, estimates the tumor dose lost with the RCR model, and gives each option’s time-corrected tumor EQD2 and late-tissue EQD2 against the plan. The defaults reproduce RCR worked example 2: 70 Gy in 35 fractions for head and neck cancer, with the sixth week missed.

    Planned course

    Tumor and late tissue

    Head and neck values from RCR 2019: tumor α/β 10 Gy, Tk 28 days, K 0.9 Gy per day. Choose another site to edit them. Late-tissue α/β: 3 Gy generic, 2 Gy for spinal cord.

    The gap

    Blank: where option 1 ends. RCR example 4 uses day 53.

    Planned overall time
    46 days
    Without compensation
    53 days
    Time-corrected tumor EQD2 change
    -

    -

    -

    Compensation options, in the RCR order of preference

      8.How the gap estimate works and where it stops

      Tumor BED = N · d · (1 + d / [α/β]) − K · (T − Tk) once the overall time T passes Tk; the late-tissue BED has no time term (RCR 2019, Appendix B; Dale 2002). T is counted in days from the first fraction (day 0) to the last, so 35 weekday fractions from a Monday give T = 46. K is the BED lost for each day of overall time after repopulation starts at day Tk. Each option first finds the days available up to the planned last day; the dose per fraction for the larger-fraction options is solved from the LQ equation, so the extra dose is not added pro rata. As in the RCR calculation steps, options 3 and 4 first set the dose per fraction to keep the late BED, then show the tumor-matched dose as the alternative. Option 4 (RCR methods 5 and 6) ends where option 1 ends unless you enter another day, and compares one fraction on each treatment day, one every day, and two fractions on alternate days; option 5 keeps the delayed schedule (Hendry 1996, method 3). The time-corrected tumor EQD2 is the tumor BED, including the repopulation term, expressed as EQD2, so a change reads directly as dose lost or regained; for 70 Gy in 35 fractions over 46 days it is 56.5 Gy. RCR examples 2 and 3 restart the day after the missed days, weekend included (the default); example 1 restarts on the Monday, so untick the restart box to match it.

      Parameters. The RCR gives values for head and neck squamous cell carcinoma; for other sites, enter values from a source for that site, or K = 0 to count days only.
      ParameterValueBasisSource
      Tumor α/β, head and neck SCC10 GyGeneric tumor value; breast and prostate cancer are exceptionsRCR 2019
      Repopulation start, Tk28 daysWorking value paired with K; accelerated repopulation from about 4 weeksDale 2002; Withers 1988
      Repopulation dose, K0.9 Gy/dayGy of BED10 lost per day after Tk. Four-centre analysis 0.89 (95% CI 0.35–1.43); two centres 0.6–0.8; other analyses 0.94–0.99. A rate quoted in Gy per day in 2 Gy fractions must be multiplied by (1 + 2 / [α/β]) before entering it as K.Dale 2002; Robertson 1998; Hendry 1994; Fu 2000 (RTOG 9003), Withers 2000 and Fowler and Harari 2000, as summarized in RCR 2019
      Late-tissue α/β3 GyGeneric late value; 2 Gy for spinal cordRCR 2019
      Twice daily≥ 6 h; ≤ 2.2 GyDays with two fractions spaced through the remaining time, not consecutive; Fridays suit well. Not recommended when the fraction size is significantly greater than 2.2 Gy (5.2); fractions of 5 Gy or more are not suitable (5.5)RCR 2019
      SABR≥ 5 Gy, ≤ 8 fxThis tool’s working definition, not an RCR one. The RCR advises resuming on non-consecutive days rather than accelerating (5.5)RCR 2019
      RCR categories for overall time (RCR 2019, section 3).
      CategoryExamplesProlongation
      1Radical treatment of squamous cell carcinoma of the head and neck, cervix, anus, skin, vagina and vulva; oesophageal cancer; non-small cell lung cancer; small cell lung cancer with chemoradiotherapy; medulloblastoma and PNET; other tumors with a short mass-doubling time. For combined external beam and brachytherapy (cervix, tongue, anus), the combined overall time countsAim for none; audit standard no more than 2 days in at least 95% of patients
      2Radical treatment of slower-growing tumors: breast, bladder and prostate cancerIdeally no more than 2 days; compensate when the extension exceeds 5 days
      3Palliative treatmentCompensation may be needed, particularly beyond 7 days

      Limits. K and Tk are population estimates with wide uncertainty, and the model is linear-quadratic with a linear repopulation term. Incomplete repair between twice-daily fractions is not modeled; it matters most for brain and spinal cord and for fractions well above 2 Gy. Bank holidays are not modeled: enter the treatment days missed. Concurrent chemotherapy does not change the calculation; the RCR suggests not giving it on the same day as accelerated compensatory treatment. For SABR the RCR advises resuming on non-consecutive days rather than accelerating. Late EQD2 is for tissue receiving the prescription dose; for an organ at risk at a different dose per fraction, rerun the tool with that dose (RCR Appendix B, step 1). Any increase in late EQD2 needs review by the treating physician and physics team before it is used.

      Key points

      • Compare schedules at both α/β values: 27 Gy / 3 matches 18 Gy × 1 for tumor (BED10 about 51 vs 50) at a lower late-CNS EQD2 (about 74 vs 90 Gy).
      • For re-irradiation, sum the dose the structure received, not the prescriptions. The remaining budget is the cumulative goal minus the prior EQD2 (with forgiveness only if the goal was built for it); solving for dose per fraction turns it into schedules. With several structures, the one that runs out first sets the ceiling.
      • Published CNS cumulative levels: brain about 100 Gy EQD2 after conventional re-irradiation; spinal cord BED 135.5 Gy2 (6 months apart, each course ≤ 98 Gy2); SBRT re-irradiation thecal sac about 70 Gy EQD2. Brainstem and optic levels are consensus or institutional values, not validated limits.
      • Use forgiveness (a recovery discount) or a raised cumulative limit, not both (the calculator flags an override); α/β = 2 is the usual default for late CNS effects (1.6 to match HyTEC optic tables).
      • After an unscheduled gap, keep the overall time where possible: weekend or bank-holiday days first, then twice-daily fractions at least 6 hours apart. Larger fractions keep the tumor dose at a higher late dose, and for head and neck cancer each day of overall time beyond day 28 costs about 0.9 Gy of tumor BED (RCR 2019).

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