MOSFET Threshold Voltage Calculator — Body Effect and Overdrive

Background.

A MOSFET's threshold voltage is not a single number. The value on the datasheet is measured with the source tied to the substrate, and the moment your source sits above the body — a stacked device, a source follower, any transistor in an IC whose body goes to the negative rail — the threshold climbs. That climb is the body effect, and it is the reason a circuit that simulates perfectly on paper can refuse to turn on when the transistor is second in a stack.

This page computes the shifted threshold from the four parameters that govern it: the zero-bias threshold V_T0, the body-effect coefficient γ, the surface potential 2Φ_F and the source-to-body voltage V_SB. It then reports the overdrive left at your gate drive, the square-law saturation current that follows from it, and χ = ∂V_T/∂V_SB — the number that tells you what each further volt of source-body bias will cost.

Two things to know before reading the answer. First, V_T0, γ and K are properties of one device on one process, not universal constants; the values shown as defaults are illustrative placeholders and should be replaced with figures from your SPICE model card or datasheet. The exception is 2Φ_F, which is close to 0.6 V for silicon and is cited below. Second, the scope is deliberately narrow: enhancement-mode n-channel, saturation region, channel-length modulation off. The current shown is valid only where V_DS is at least the overdrive; the triode region is not modelled here, because neither of the two sources this page is built on states the triode equation, and a formula nobody published is not one worth guessing.

What is mosfet threshold voltage calculator?

The threshold voltage is the gate-to-source voltage at which an inversion layer forms and the channel starts to conduct. Below it the transistor is off; above it the drain current rises with the square of the excess. The body, or substrate, is a fourth terminal, and reverse-biasing the source-body junction widens the depletion region under the channel, so more gate charge is needed before inversion happens. Formally, V_T = V_T0 + γ(√(2Φ_F + V_SB) − √(2Φ_F)), where V_T0 is the threshold with the source at body potential, γ is the body-effect coefficient set by substrate doping and gate-oxide capacitance, and 2Φ_F is the surface potential. Because the relation is a square root, the sensitivity falls as V_SB grows: the derivative χ = γ/(2√(2Φ_F + V_SB)) is largest near zero bias. In discrete MOSFETs the body lead is bonded to the source inside the package, so V_SB is zero and there is no body effect at all — which is why the effect surprises people who move from board-level design to integrated design.

How to use this calculator.

1. 01Enter the zero-bias threshold V_T0 from the datasheet or the SPICE model card, not from memory — it is device-specific.
2. 02Enter the body-effect coefficient γ and the surface potential 2Φ_F. SPICE calls them GAMMA and PHI. Use 0.6 V for 2Φ_F on silicon if you have nothing better.
3. 03Enter the source-to-body voltage V_SB. Use zero for a discrete part, where the body is tied to the source internally.
4. 04Enter the gate drive V_GS and the transconductance coefficient K, remembering that K here is defined so that I_D = K(V_GS − V_T)².
5. 05Read the shifted threshold and the overdrive. If the overdrive is zero or negative, the device is off at this gate drive.
6. 06Read χ. It is the volts of threshold per volt of body bias, and it is also g_mb/g_m — the strength of the substrate as a second gate.

The formula.

Take the worked example: V_T0 = 0.7 V, γ = 0.5 √V, 2Φ_F = 0.6 V, V_SB = 1 V. The two square roots are √1.6 = 1.264911 and √0.6 = 0.774597, and their difference is 0.490314. Multiply by γ and the body effect has added 0.2451571974 V, taking the threshold from 0.7 V to 0.9451571974 V. That is a 35 % increase in threshold from one volt of source-body bias, and it is entirely invisible on the datasheet.

With a gate drive of 3 V, the overdrive is 3 − 0.9451571974 = 2.0548428026 V. Squaring it and multiplying by K = 1 mA/V² gives a saturation drain current of 4.2223789433 mA. Had the body effect been ignored, the overdrive would have been 2.3 V and the current 5.29 mA — a 25 % overestimate from a 0.245 V error in the threshold, because the square law amplifies it.

The sensitivity is χ = γ/(2√(2Φ_F + V_SB)) = 0.5/(2 × 1.264911) = 0.1976423538. That sits inside the 0.1 to 0.3 range published as typical, and it says the next volt of body bias will cost roughly another 198 mV of threshold — less than the first volt cost, because the square root is flattening. A test differentiates the threshold expression numerically and checks it against this closed form, so the two cannot drift apart.

Rounding happens once, at the return boundary, to ten decimal places; every intermediate square root is carried at full precision. Both classification bands — whether the device conducts, and whether χ is inside the published typical range — read the unrounded values.

One convention needs stating because textbooks disagree. This page defines K so that I_D = K(V_GS − V_T)², which is Georgia Tech's ECE 3050 notes and matches the ½µC_ox(W/L) form used in the Toronto notes. As those same Georgia Tech notes point out, some texts define K without the one-half, writing I_D = (K/2)(V_GS − V_T)², in which case their K is twice the one entered here. If your source uses that form, halve the value.

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.