Stereotactic Radiosurgery · Calculator

Dose Calculator

BED and EQD2, re-irradiation sums, and dose falloff around a target

Three tools for the questions that come up at the planning station: how two schedules compare, how much room a previously irradiated structure has left and which schedules fit in it, and how fast dose leaves a target of a given size. Each tool states its model and its sources. This is an educational tool, not a planning system; clinical decisions follow the treatment plan and the constraint set adopted by your physics and radiation-oncology team.

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

Orientation

All three 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). Use the numbers to compare schedules and to check reasoning, not to set a dose. The trial schedules and normal-tissue limits behind these tools are on the Dose Tables page; conformity and gradient indices are defined on Plan-Quality Metrics; 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.

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

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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, 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 lists the largest prescription that fits for 1 to 30 fractions. Add up to three more structures and each schedule is capped by whichever runs out first.

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)
    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

    Dose Falloff Around a Target

    6.Pre-plan falloff estimate

    Before a plan exists, the falloff can be estimated from three numbers: target size, prescription, and the Paddick gradient index (GI = volume inside the half-prescription isodose / volume inside the prescription isodose). When no plan GI is available, the tool fills in a typical published value for the platform and target size. The prescription isodose line sets the hot spot inside the target; the GI sets how fast dose falls outside it.

    1.0 = the prescription isodose matches the target exactly. Enter the plan value if known.

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    Maximum dose (Rx / isodose line)
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    Prescription to half-prescription distance
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    Dose 1 mm outside
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    Dose 2 mm outside
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    Dose 3 mm outside
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    Brain + target V12
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    • Target
    • Prescription isodose, when larger than the target
    • Inside half-prescription isodose
    • 12 Gy line
    • 1, 2, and 3 mm from the target edge

    7.How the estimate works

    The target is treated as a sphere, and the prescription isodose as a concentric sphere sized by the volume ratio you enter (1.0 means it matches the target exactly; real plans are usually somewhat larger). Outside it, dose falls as D(r) = Rx · (Rp / r)k, where Rp is the radius of the prescription isodose and k = 3 · ln 2 / ln GI, which makes the half-prescription volume exactly GI times the prescription volume. The same curve gives the dose 1–3 mm out, the prescription-to-half-prescription distance (Paddick’s gradient measure), and the volume inside the HyTEC brain threshold for the selected schedule (V12 for 1 fx, V20 for 3 fx, V24 for 5 fx, each including the target). Real plans are not spheres; multiple targets add overlapping low dose; and coverage, conformity, collimation, and energy all move the GI. Treat the output as an order-of-magnitude check, never as a substitute for the plan. The rough GI range is ±0.3 for targets of 1 cc or more (the regression’s residual standard error was 0.29) and is widened by judgment for smaller targets.

    Typical published GI by target volume. The linac column follows the Popescu-Bârhală regression (TrueBeam HD-MLC, 200 targets; adds about 0.2 when several targets share one plan). HyperArc was not part of that regression; Liu 2021 HyperArc medians are shown for comparison. Multi-platform benchmarks: Vergalasova 2019 and Paddick 2023; compare plans at a fixed coverage when reading GI (Ohtakara 2011). The Gamma Knife column is a synthesis of cohort medians and means (vestibular schwannoma and metastasis series) and is less precise below 0.5 cc. The 1 cc and larger anchors lean on Shin’s schwannoma plans (12–13 Gy, mean Paddick conformity index 0.58); low conformity lowers GI, so well-conformed plans may run somewhat higher.
    Target volumeGamma KnifeLinac (TrueBeam)Reported values behind the estimate
    < 0.1 ccabout 4.0about 6–7Few data; wide spread on every platform
    0.1–0.5 ccabout 3.6about 5.0≤ 0.4 cc medians: Gamma Knife 3.75, HyperArc 4.96 (Liu 2021)
    0.5–1 ccabout 3.1about 3.9> 0.4 cc medians: Gamma Knife 3.19, HyperArc 3.30 (Liu 2021)
    1–3 ccabout 2.8about 3.2Gamma Knife 1–3 cc mean 2.68 (Shin 2026)
    3–10 ccabout 2.65about 2.6Gamma Knife ≥ 3 cc mean 2.64 (Shin 2026); no significant platform difference above 2.5 cc (Chea 2021)
    > 10 ccabout 2.6about 2.3Linac value from the regression; few Gamma Knife data at this size
    Reading GI across platforms GI is normalized to the prescription dose, so the prescription isodose line does not enter its formula. The isodose line does change the gradient itself: prescribing lower on the dose profile steepens the falloff and makes the center hotter (Gamma Knife falloff was steepest near the 40% line in Paddick and Lippitz; with dynamic conformal arcs, GI rose from 3.9 to 5.7 as the line moved from 55% to 90% in Chea 2021). Fair comparisons match target size and coverage, read GI alongside a conformity index (a plan whose prescription isodose spills beyond the target can show a deceptively low GI), and report absolute V12. Head-to-head studies generally find a lower GI with Gamma Knife for small targets and little or no difference above about 2.5 cc (Chea 2021); in Liu 2021, HyperArc matched Gamma Knife on conformity and normal-tissue V12 above about 0.4 cc.
    Part IV

    Common Schedules

    8.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. Load sends a schedule to 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

    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).
    • The isodose line sets the hot spot (prescribing to 50% doubles the center dose); the gradient index sets how fast dose leaves the target. Small targets have higher GI on every platform.
    • A pre-plan falloff estimate is a sanity check for V12 and nearby structures; the treatment plan is the answer.

    Last updated November 2026.

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