Radiation Dose Calculator
The formula
What the biologically effective dose tells you
The linear-quadratic BED/EQD2 conversion radiotherapy uses to compare schedules with different fraction sizes on one scale.
Calculation: BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β). Enter your inputs and every substitution is shown below the result.
Reading the result
BED converts fractionation; EQD2 restates any course as if it were given at 2 Gy — hypofractionation trials speak this language.
Rules of thumb: Prostate SBRT BED10 >100; lung SABR BED10 >100 correlates with control
Limitations and best practice
BED assumes repair parameters constant across the course and ignores repopulation gaps — overall time corrections are separate.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Why α/β 10 vs 3?
Does this replace planning?
Source & methodology
Fowler BED/EQD2 radiobiology; QUANTEC.
How Radiation Dose works — and what your result really means
Health numbers only mean something against a reference — this page gives you both the number and the band it sits in. Searchers land on a Radiation Dose page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
People rarely disagree about arithmetic; they disagree about assumptions that were never written down. Printing the substitution and the sensitivity ranking removes that category of disagreement for Radiation Dose.
Most confusion about Radiation Dose comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to BED = 92.4 Gy10 on the default inputs, and the sensitivity section ranks the inputs that move the result — Total dose first, at ≈10.0 % of the headline for a ten-percent error either way in that input — which is the thread the rest of this guide pulls on.
Inside the Radiation Dose calculation: formula and every input
The engine implements a single stated model: BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β). There is no hidden coefficient and no login-gated precision — the formula printed is the formula executed, which is also what makes the result citable.
Total dose (Gy) (example value 77) is a quantity rather than a category — precision here is cheap and worth having. Double-check that the unit on your source matches the unit this field expects before typing.
Dose per fraction (Gy) (example value 2) is a quantity rather than a category — precision here is cheap and worth having. Take this figure from a label, a report or a prescription — never from a guess.
Tissue α/β (example value Tumour (~10)) is a selector, not a measurement: the engine follows a different route for each option. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
What each “Tissue α/β” choice actually does: Tumour (~10) → 92.4 Gy10 · Late normal tissue (~3) → 128.3 Gy10 · Early reacting (~10) → 92.4 Gy10 These figures are computed from this engine, not estimated — switch the dropdown above and you will land on exactly these numbers.
Radiation Dose with real numbers, step by step
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Total dose (Gy), Dose per fraction (Gy), Tissue α/β. The endpoint of that chain is 92.4 Gy10 of BED, sitting in the “2.00 Gy × 39 fractions = BED 92.4Gy10 and EQD2 77.0 Gy in 2-Gy terms — the currency that makes hypofractionation regimens comparable” band.
- n = 77 ÷ 2.00 = 39
- BED = 77 × (1 + 2.00/10) = 92.4
- EQD2 = 77 × (2.00 + 10)/(2 + 10) = 77.0
Fractions — 39. This is the number experienced users quote when the headline alone would mislead.
EQD2 (2 Gy) — 77.0 Gy. Compare it against the main result of 92.4 Gy10 before drawing conclusions.
Equivalent course — 38.5 × 2 Gy. If your inputs change, this is usually the first companion figure to move.
Therapeutic ratio — compare tumour BED10 vs organ BED3, never mix. Read next to the headline, this is the figure that shows the shape of the trade-off.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
Scenario table: Radiation Dose at ±10 % and ±20 % of the key input
The honest version of any estimate is a corridor, and this one is cheap to produce: Radiation Dose was recomputed at 5 points along the dominant input, with every other field left untouched.
| Total dose setting | BED |
|---|---|
| 80 % of the example value | 73.9 Gy10 |
| 90 % of the example value | 83.2 Gy10 |
| example inputs | 92.4 Gy10 |
| 110 % of the example value | 101.6 Gy10 |
| 120 % of the example value | 110.9 Gy10 |
Across 5 settings of Total dose, the result spans 73.9 Gy10 to 110.9 Gy10. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Total dose alone; the substitution steps will follow your figures exactly.
Where Radiation Dose is fragile — and where it is not
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the BED was recalculated from scratch. Read it as a map of where Radiation Dose is fragile — drawn for the example inputs, which is the map you want when deciding what to measure carefully.
- Total dose: ten percent up gives 101.6 Gy10, ten percent down gives 83.2 Gy10 — ≈10.0 % of the BED either way
- Dose per fraction: ten percent up gives 93.9 Gy10, ten percent down gives 90.9 Gy10 — ≈1.7 % of the BED either way
Total dose is the dominant lever here: ten percent either way moves the result by about 10.0 %, from 83.2 Gy10 to 101.6 Gy10. Spend your verification effort there first, and treat Dose per fraction as the second priority (≈1.7 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
What a Radiation Dose of 92.4 Gy10 means in practice
A number on its own is trivia; a number against a range is intelligence. On the example inputs the band reads “2.00 Gy × 39 fractions = BED 92.4Gy10 and EQD2 77.0 Gy in 2-Gy terms — the currency that makes hypofractionation regimens comparable”; your own figures place you on a different rung of the same ladder. Before treating the band as fact, note its width: ten percent either way on Total dose already spans 83.2 Gy10 to 101.6 Gy10. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Related measures answer related questions, and the distinctions matter: Radiation Dose is the quantity, BED is this tool’s reading of it, and the decision that follows belongs to neither of them separately.
Why Radiation Dose results go wrong — and how to prevent it
BED assumes repair parameters constant across the course and ignores repopulation gaps — overall time corrections are separate. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Comparing a Radiation Dose computed here with a figure from another source that uses different conventions. Same name, different denominator — the disagreement is usually in the definitions, not the data.
This model has its own particular trap: Total dose carries ≈10.0 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: a Radiation Dose computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Radiation Dose verification checklist
- Compare the output against one published benchmark or a colleague’s independent estimate.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Check Total dose before anything else: it is the measured dominant input, ≈10.0 % of Radiation Dose per ten percent.
- Compare the result with one independent method or published benchmark.
- Confirm the example values are plausible for your own situation before replacing them.
- Repeat the ±10 % test on the inputs that matter and see whether the decision — not just the number — still holds.
Step by step: getting a trustworthy Radiation Dose out of this tool
Using a calculator well sounds trivial, but the difference between a decision-grade figure and a throwaway one lives entirely in the routine. The routine for Radiation Dose takes a minute to learn and applies to every input above.
Step 1 — start from evidence. The inputs behind Radiation Dose are total dose (gy), dose per fraction (gy), tissue α/β. Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. Estimates improve most when the worst case is written down in ink.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. Note the assumption you are least sure about; that is where the real risk lives.
Step 3 — play with the inputs on purpose. Ten percent up, ten percent down, one field at a time. Within a few minutes you will know this calculation better than most people who quote its results. When two sources disagree, it is almost never the arithmetic that differs.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 5 — record the context, not just the number. Note today’s date and the inputs alongside the 92.4 Gy10 output. Six months from now the context is what turns this figure into a trend. Compare the calculation to the rough guess you arrived with, and ask why they differ.
Who actually uses Radiation Dose — and when
Numbers earn their keep in conversations, and Radiation Dose is no exception. In Health & Medical discussions around Medications & Dosing, this figure decides whether an option stays on the table: it converts an opinionated debate into an arithmetic one, and arithmetic is the only referee both sides accept. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Professionals in Medications & Dosing use this style of calculation as a screening filter before spending real money or effort: a quick Radiation Dose check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. If the verdict changes with a ten-percent nudge, report the nudge alongside the number.
Treat Radiation Dose like a smoke alarm rather than a painting — its value is in being tested periodically, not in being admired once. A figure with a date beside it becomes evidence; without one it stays an anecdote.
Radiation Dose — frequently asked questions
What affects Radiation Dose the most?
Radiation Dose is driven above all by Total dose. Perturbing only that field by ten percent either way produced 101.6 Gy10 against the 92.4 Gy10 baseline — a ≈10.0 % response, while Dose per fraction manages ≈1.7 %.
Which matters more: dose per fraction or total dose?
Total dose, by a factor of about 6.0. Concretely: ten percent on Total dose is worth ≈10.0 % of Radiation Dose, the same nudge on Dose per fraction only ≈1.7 %. That ranking is re-computed for each page from that page’s own defaults.
How much does the “Tissue α/β” choice change the answer?
A great deal, on these inputs: Radiation Dose comes out at 92.4 Gy10 on the lowest option (“Tumour (~10)”) and 128.3 Gy10 on the highest (“Late normal tissue (~3)”). Each option is listed with its computed value so you can see what the choice is worth before you make it.
What is a typical Radiation Dose?
There is no honest universal average for Radiation Dose, but there is a reference point: the defaults on this page produce 92.4 Gy10 (2.00 Gy × 39 fractions = BED 92.4Gy10 and EQD2 77.0 Gy in 2-Gy terms — the currency that makes hypofractionation regimens comparable). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Radiation Dose by hand?
Use the stated model — BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β) — and substitute in the order the tool prints (it starts from n = 77 ÷ 2.00 = 39). On the example inputs the hand route lands on 92.4 Gy10, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Radiation Dose if total dose changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the BED goes across 83.2 Gy10 to 101.6 Gy10, a swing of roughly 10.0 % around the 92.4 Gy10 baseline. That ratio is the practical definition of how much this input matters.
Is the Radiation Dose result of 92.4 Gy10 good or bad?
Neither, on its own — the label “2.00 Gy × 39 fractions = BED 92.4Gy10 and EQD2 77.0 Gy in 2-Gy terms — the currency that makes hypofractionation regimens comparable” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Total dose alone moves it by ≈10.0 %.
Is Radiation Dose accurate?
The arithmetic is exact: BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β) is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 92.4 Gy10 result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Can Radiation Dose be negative or empty?
Yes, and that is informative rather than broken: a negative Radiation Dose usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Why α/β 10 vs 3?
Tumours/early tissue behave linearly with fraction size (high α/β); late-responding normal tissue is fraction-size sensitive (low).
Does this replace planning?
Never — it complements DVH metrics for schedule comparison.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
The vocabulary of Radiation Dose
- Fractions
- 39 on the example inputs — a companion figure printed beside the headline of Radiation Dose so that no result is read in isolation.
- EQD2 (2 Gy)
- 77.0 Gy for the Radiation Dose worked case; it sits next to the main result because it carries context the headline leaves out.
- Equivalent course
- 38.5 × 2 Gy on the example inputs — a companion figure printed beside the headline of Radiation Dose so that no result is read in isolation.
- BED
- The primary output of this tool: 92.4 Gy10 for the default inputs, computed exactly from BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β).
- Worked example
- Every substitution in order, from the example inputs to 92.4 Gy10 — the audit trail for the headline figure.
- Verdict band
- The interpretation attached to a result (“2.00 Gy × 39 fractions = BED 92.4Gy10 and EQD2 77.0 Gy in 2-Gy terms — the currency that makes hypofractionation regimens comparable” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Radiation Dose moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Methodology, sources and limits
Everything above runs on one stated formula, applied without hidden coefficients: BED = nd(1 + d/(α/β)); EQD2 = D × (d+α/β)/(2+α/β). Source of record: Fowler BED/EQD2 radiobiology; QUANTEC. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. The sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
What to do with your Radiation Dose next
Re-measure on a second occasion before changing behaviour; single readings carry natural day-to-day variation.
Whoever you are (people checking a personal health figure before acting on it), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Health & Medical, a dated figure is a trend, and an undated one is a rumour.