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Radiation Oncology

NSD Calculator (Ellis Formula)

Radiobiology History: NSD (Ellis Formula)

Historical Parameters

*T includes weekends and holidays from day 1 to last day.

Historical Archive

Analyze treatment plans using the first mathematical model of dose-time-fractionation in oncology history.

Guidelines & Evidence

Verified

Last Review: 2026

Radiobiology History

The Ellis Formula

Proposed by Frank Ellis in 1969, the NSD was the first widely adopted mathematical model to account for the three primary variables in radiotherapy: Total Dose, Number of Fractions, and Overall Treatment Time. It was based on observations of skin reaction tolerance and was the precursor to all modern radiobiological modeling.

The NSD Equation

$$NSD = rac{D}{N^{0.24} imes T^{0.11}}$$ Where: D = Total Dose (rads/cGy), N = number of fractions, T = overall treatment time in days.

Ret Unit

The resulting unit of NSD is the ret (Rad Equivalent Therapy). An NSD of 1800 rets was considered the tolerance limit for normal connective tissue.

Last Comprehensive Review: 2026