MOSFET Threshold Voltage Calculator — Body Effect and Overdrive

Background.

Ask a datasheet for an n-channel MOSFET's threshold and you get one number, measured with the source connected to the body. Inside an integrated circuit that condition rarely holds. The substrate is shared by every transistor on the die and sits at the most negative rail, so any device whose source rides above that rail, such as the upper transistor in a cascode or a source follower, has a reverse-biased source-body junction. The depletion region under the channel widens, the gate must hold more charge before an inversion layer forms, and the threshold climbs. That is the body effect.

The climb follows a square root. With a zero-bias threshold of 0.7 V, a body-effect coefficient of 0.5 √V and a surface potential of 0.6 V, one volt of source-body bias adds 0.2452 V, a 35 percent rise. Five volts add 0.7959 V: more, but nowhere near five times as much.

Add the gate drive and the calculator also reports the overdrive, the square-law saturation current and χ, the slope of threshold against bias, using the long-channel hand-analysis model with channel-length modulation ignored.

What is mosfet threshold voltage calculator?

The threshold voltage is the gate-to-source voltage at which an inversion layer forms under the gate and the channel begins to conduct. The body is the transistor's fourth terminal, and its potential relative to the source sets how much depletion charge the gate must overcome. The coefficient γ equals √(2qN_Aε_S) ÷ C_ox, so it grows with substrate doping and shrinks with a thinner, higher-capacitance gate oxide. The surface potential 2Φ_F is close to 0.6 V for silicon. SPICE model cards call the three parameters VTO, GAMMA and PHI.

How to use this calculator.

1. 01Enter V_T0, γ and 2Φ_F from the SPICE model card or process documentation; the defaults are placeholders.
2. 02Enter V_SB, the source voltage minus the substrate voltage. It is zero for a discrete part, where the body is bonded to the source inside the package.
3. 03Enter the gate drive V_GS and the coefficient K. Here K multiplies the squared overdrive directly, K = ½µC_ox(W/L); if your textbook writes I_D = (K/2)(V_GS − V_T)², halve its K first.
4. 04Compare V_DS in your circuit with the overdrive. The drain current shown applies only when V_DS is at least V_OV, the saturation region.

The formula.

V_T = V_T0 + γ(√(2Φ_F + V_SB) − √(2Φ_F)). The square roots come from the depletion layer under the channel: its charge grows with the square root of the voltage across it, and γ converts that charge into gate voltage by dividing by the oxide capacitance. Subtracting √(2Φ_F) makes the shift zero when V_SB is zero, so V_T0 is recovered exactly. Some notes write the same law with the body-to-source voltage, √(φ − v_BS); the sign flips cancel and the numbers agree. The overdrive is V_OV = V_GS − V_T, and the saturation current is I_D = K·V_OV² when V_OV is positive, zero otherwise. The body factor χ = γ ÷ (2√(2Φ_F + V_SB)) is the derivative of V_T with respect to V_SB, so it is largest at zero bias and falls as bias grows. Because the current depends on the square of the overdrive, a small percentage error in the overdrive roughly doubles by the time it reaches I_D.

A worked example.

Frequently asked questions.

References& sources.

1. [1]W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering — ECE 3050 course notes, 'The MOSFET: Device Symbols, Device Equations', © 2010. Primary source for the equations implemented. Eq (1): v_TH = V_TO + γ(√(φ − v_BS) − √φ), 'where VTO is the value of vTH with vBS = 0, γ is the body threshold parameter, φ is the surface potential, and vBS is the body-source voltage'. Eq (2) and (6): i_D = (k′/2)(W/L)(1 + λv_DS)(v_GS − v_TH)² = K(v_GS − v_TH)². Region condition: 'The n-channel MOSFET is biased in the active mode or saturation region for v_DS ≥ v_GS − v_TH'. Cutoff: 'For v_GS ≤ V_TO, the drain current is zero.' Also the explicit warning about the competing K convention: 'Some texts define K = k′(W/L)(1 + λv_DS) so that i_D is written i_D = (K/2)(v_GS − v_TH)². In this case, the numerical value of K is twice the value used here.' PDF. Retrieved 2026-07-29.
2. [2]MIT OpenCourseWare, 6.720J Integrated Microelectronic Devices, Lecture 24, page 9, independently confirms Vth(VSB) = Vth(VSB = 0) + γ[√(φsth + VSB) − √φsth] and the direction VSB ↑ ⇒ Vth ↑. David Johns, University of Toronto, ECE331 lecture notes, 'Body Effect for MOS Transistors', Eq. (5), was separately consulted for the diagnostic χ band of 0.1 to 0.3; that source is recorded bibliographically because its host no longer answers the citation resolver. The two sign conventions are algebraically identical and agree on every value this page computes. Retrieved 2026-07-29.
3. [3]James M. Fiore, 'Semiconductor Devices: Theory and Application', §12.4 'The E-MOSFET', Engineering LibreTexts (open-access textbook). Third treatment, used to confirm the square-law form independently of the two lecture-note sources: Equation 12.5 gives I_D = k(V_GS − V_GS(th))², with k described as 'a device parameter (a constant, units of amps/volt² or siemens/volt)', and Equation 12.6 gives the transconductance g_m = 2k(V_GS − V_GS(th)). This is the same convention this page uses for K, confirming that the factor of one-half belongs inside the coefficient. Retrieved 2026-07-29.