// multi-utility computation suite · offline · instant · precise
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sci.gradient-echo-TR-TE-flip Calculator
Calculates flip angle, TR, TE and signal intensity for gradient echo MRI sequences from tissue T1, T2*, and proton density. FLASH sequence: optimal flip angle (Ernst angle) = arccos(exp(−TR/T1)) — at TR = 100 ms and T1 = 800 ms, Ernst angle ≈ 14°.
Inputs
Tr Ms
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Te Ms
Duration of the process. Make sure units match the rate inputs (seconds, minutes, or hours).
Flip Deg
Reference formula or conversion factor shown for context.
T1 Ms
Reference formula or conversion factor shown for context.
T2Star Ms
Reference formula or conversion factor shown for context.
Results
relative signal Mxy
The meaningful information component, separated from noise.
Ernst angle α_opt (deg)
The computed angle in degrees or radians.
T2* decay factor exp(−TE/T2*)
A dimensionless multiplier applied in the calculation.
T1 recovery factor exp(−TR/T1)
A dimensionless multiplier applied in the calculation.
Ernst angle: cos(α) = exp(−TR/T1)
The computed angle in degrees or radians.
contrast weighting
The computed weight (gravitational force) or mass.