Free BED Calculator

Biologically Effective Dose Calculator

The Biologically Effective Dose (BED) calculator—serving also as an EQD2 Calculator and Radiotherapy Dose Calculator—offers a straightforward method to assess the biological impact of any radiation fractionation schedule. Relying on the well‑established BED Formula, this tool returns both the biologically effective dose and the Equivalent Total Dose in 2‑Gy fractions (EQD₂), enabling direct comparison between different treatment plans.

Parameters Required

To compute the BED and EQD₂, the user must specify:

• Irradiation duration – either short (standard) or prolonged. For prolonged exposure, an additional dose‑rate factor $g$ (0 < $g$ < 1) is required to account for the repairability of cells.
• α/β ratio (Gy) – a tissue‑specific measure of radiosensitivity. Common reference values include:
  • Late‑reacting tissues: $\alpha/\beta \approx 3\ \text{Gy}$
  • Early‑reacting tissues: $\alpha/\beta \approx 10\ \text{Gy}$
  • Central nervous system and kidneys: $\alpha/\beta \approx 2\ \text{Gy}$
• Dose per fraction ($d$, Gy) – the radiation dose delivered in a single session.
• Total dose ($D$, Gy) – the sum of all fractions, equivalent to $n \times d$.

All results are expressed in grays (Gy), the SI unit for absorbed dose.

Standard and Slow‑Delivery BED Formulas

The fundamental BED equation, based on the linear‑quadratic survival model, is:

$$\text{BED} = D \times \left(1 + \frac{d}{\alpha / \beta} \right)$$

For fractions delivered over more than a few minutes, the formula is adjusted to:

$$\text{BED} = D \times \left(1 + \frac{g \cdot d}{\alpha / \beta} \right)$$

where $g$ denotes the dose‑rate factor for intracellular repair. Both equations capture the contribution of dose protraction to the overall biological effect.

Equivalent Total Dose in 2‑Gy Fractions (EQD₂)

To facilitate comparison with conventional 2 Gy per‑fraction treatments, the calculator converts any regimen into the EQD₂:

$$\text{EQD}_{2} = D \times \frac{d + \alpha / \beta}{2 + \alpha / \beta}$$

This metric is widely used in clinical trials and meta‑analyses to pool data from different fractionation schemes.

Clinical Considerations

BED is a standard tool in radiobiology for comparing alternative fractionation protocols and for reporting research findings. For optimal accuracy, separate BED calculations should be performed for each type of tissue (tumor, surrounding organs) using its specific α/β ratio; the overall treatment effect is the sum of these individual BED values. Note: BED should never be confused with the biological equivalent dose—these are distinct concepts in radiation therapy.

Disclaimer

This Biologically Effective Dose Calculator is intended for educational and planning purposes. It does not replace the comprehensive evaluation performed by a radiation oncologist or medical physicist. For any medical condition, please consult a qualified healthcare provider.