MOSFET Threshold Voltage Calculator
Find MOSFET drain current in any operating region or calculate the gate voltage needed to achieve a target current. Uses the standard square-law MOSFET model.
⚡ What is MOSFET Threshold Voltage?
MOSFET threshold voltage (Vth) is the minimum gate-to-source voltage at which the transistor forms an inversion layer in the channel and begins conducting between drain and source. Below Vth the device is in cutoff and essentially no current flows. Above Vth the channel opens and current scales with the square of the overdrive voltage (Vgs minus Vth). This square-law relationship is the foundation of both analog amplifier biasing and digital switching circuit design.
The threshold voltage appears in three key design calculations. First, in switching power supplies and motor drivers, the gate driver voltage must reliably exceed Vth under all conditions (including cold start and high temperature variation) to turn the MOSFET fully on. Second, in analog amplifiers and current mirrors, the bias voltage is set a specific overdrive above Vth to achieve a target transconductance and drain current. Third, in load-switch and hot-swap controller circuits, Vth determines the minimum control voltage at which current begins to flow and whether resistive turn-on is possible without a charge pump.
A common confusion is between threshold voltage and the gate voltage needed to drive the MOSFET fully on. The threshold is the turn-on point; the fully-on condition requires Vgs well above Vth. Power MOSFETs specify Rds_on at Vgs = 10 V because at Vgs = Vth the device is barely conducting and Rds_on is enormous. Using the threshold voltage as the operating gate voltage in a switching circuit leads to extreme conduction losses and thermal failure.
This calculator uses the standard square-law MOSFET model from Sedra-Smith and Razavi textbooks. The model is accurate for hand calculations and SPICE-level first-order analysis. It does not account for channel-length modulation (lambda), velocity saturation, or body effect, which are second-order corrections needed only for advanced IC design verification.
📐 Formulas
Cutoff (VGS below Vth): ID = 0
Saturation (VGS > Vth and VDS ≥ Vov): ID = (KP / 2) × (VGS − Vth)²
Linear (VGS > Vth and VDS below Vov): ID = KP × [(VGS − Vth) × VDS − VDS² / 2]
Vth = threshold voltage (V) - minimum Vgs for channel formation
Vov = VGS − Vth = overdrive voltage (V)
KP = μn × Cox × W/L = process transconductance parameter (A/V² or mA/V²)
Reverse (find Vgs): VGS = Vth + √(2 × ID / KP) for saturation
Example: Vgs=5 V, Vth=2 V, KP=100 mA/V², Vds=5 V → Vov=3 V, saturation → ID = (100/2) × 9 = 450 mA
📖 How to Use This Calculator
Steps
1
Choose the calculation mode - select Find Drain Current to compute Id given all operating voltages, or Find Required Vgs to determine the gate voltage needed for a specific current in the saturation region.
2
Enter the threshold voltage Vth - find Vgs(th) on the MOSFET datasheet, typically given at a small test current (often 250 uA or 1 mA). Logic-level devices have Vth of 1 to 2 V; standard power MOSFETs have Vth of 2 to 5 V.
3
Enter Vgs, Kp, and Vds (Find Drain Current mode) - type the actual gate-source voltage, the process transconductance Kp in mA per volt squared (estimate from the datasheet transfer curve if not listed), and the drain-source voltage. The calculator automatically determines the operating region.
4
Read and apply the results - check that the operating region matches your intent (saturation for amplifiers, linear for low-resistance switches). The overdrive voltage and minimum Vds for saturation are shown as secondary results for circuit verification.
💡 Example Calculations
Example 1 - N-Channel MOSFET Switch in Saturation (Vgs=5V, Vth=2V)
Vgs = 5 V, Vth = 2 V, Kp = 100 mA/V², Vds = 5 V
1
Overdrive voltage: Vov = Vgs - Vth = 5 - 2 = 3 V. Since Vov > 0 the device is ON.
2
Check region: Vds (5V) ≥ Vov (3V) → saturation. Id is independent of Vds in this region.
3
Drain current: Id = (Kp/2) × Vov² = (100/2) × 9 = 50 × 9 = 450 mA
Result: ID = 450 mA, Region = Saturation, Vov = 3 V
Try this example →Example 2 - MOSFET in Linear Region (Low Vds Switch)
Vgs = 5 V, Vth = 2 V, Kp = 100 mA/V², Vds = 1 V
1
Overdrive: Vov = 5 - 2 = 3 V. Check region: Vds (1V) is below Vov (3V) → linear (triode) region.
2
Linear current: Id = Kp × [(Vov × Vds) - Vds²/2] = 100 × [3 × 1 - 0.5] = 100 × 2.5 = 250 mA
3
On-resistance estimate: Rds_on = Vds / Id = 1 V / 0.25 A = 4 ohms. Lower Kp or higher Vov reduces Rds_on.
Result: ID = 250 mA, Region = Linear (Triode)
Try this example →Example 3 - Logic-Level MOSFET at 3.3 V Drive (Vth=1.5V)
Vgs = 3.3 V, Vth = 1.5 V, Kp = 200 mA/V², Vds = 5 V
1
Overdrive: Vov = 3.3 - 1.5 = 1.8 V. Check region: Vds (5V) ≥ Vov (1.8V) → saturation.
2
Drain current: Id = (200/2) × 1.8² = 100 × 3.24 = 324 mA. This MOSFET is suitable for a 3.3 V logic output gate driver.
3
Transconductance: gm = Kp × Vov = 200 × 1.8 = 360 mA/V, useful for amplifier voltage gain calculations.
Result: ID = 324 mA, Vov = 1.8 V, Saturation
Try this example →Example 4 - Find Vgs for 100 mA (Find Required Vgs Mode)
Target Id = 100 mA, Vth = 1.5 V, Kp = 50 mA/V²
1
Use saturation formula rearranged: Vgs = Vth + sqrt(2 × Id / Kp)
2
Substitute: Vgs = 1.5 + sqrt(2 × 0.1 / 0.05) = 1.5 + sqrt(4) = 1.5 + 2 = 3.5 V
3
Vds must be at least Vov = 2 V to stay in saturation. Gate driver must supply at least 3.5 V reliably.
Result: Required Vgs = 3.500 V, Vov = 2.000 V
Try this example →❓ Frequently Asked Questions
What is MOSFET threshold voltage and why does it matter?
The threshold voltage (Vth) is the minimum gate-to-source voltage at which the MOSFET begins to conduct. Below Vth the device is in cutoff and Id = 0. Above Vth current flows. In switching circuits the gate driver voltage must significantly exceed Vth to turn the device on fully and minimise on-resistance. Typical N-channel enhancement MOSFETs have Vth between 1 and 5 V. Datasheets list it as Vgs(th) at a specified test drain current.
What is the square-law drain current formula for a MOSFET?
In saturation (Vds >= Vov): Id = (Kp / 2) times (Vgs - Vth) squared. In the linear region (Vds < Vov): Id = Kp times [(Vgs - Vth) times Vds - Vds squared divided by 2]. Kp = mu_n times Cox times W/L. The saturation formula applies to amplifier biasing; the linear formula applies when the MOSFET is used as a low-resistance switch with a small Vds.
What is overdrive voltage and how does it affect drain current?
Overdrive voltage is Vov = Vgs - Vth. In saturation, Id = (Kp / 2) times Vov squared. Because drain current scales with Vov squared, small changes in gate voltage produce large changes in current near threshold. At Vov = 3 V and Kp = 100 mA per volt squared: Id = 450 mA. At Vov = 2 V (same Kp): Id = 200 mA. In switching designs, maximise Vov (use a gate driver with adequate output voltage) to minimise Rds_on and conduction losses.
What are the three operating regions of a MOSFET?
Cutoff: Vgs less than Vth, Id = 0, device is off. Saturation: Vgs greater than Vth and Vds greater than or equal to Vov, Id depends only on Vgs and is nearly constant with Vds. This region is used for amplification and current sourcing. Linear (triode): Vgs greater than Vth and Vds less than Vov, Id depends on both Vgs and Vds. The device acts as a small resistance proportional to 1 divided by (Kp times Vov). Switching circuits use the linear region for the fully-on state.
How do I find Kp for my MOSFET?
Kp is rarely stated directly on datasheets. Estimate it from the transfer characteristic curve: pick two points (Vgs1, Id1) and (Vgs2, Id2) in saturation, then Kp = 2 times Id divided by (Vgs - Vth) squared. Alternatively, read the SPICE model KP parameter. Typical values are 50 to 200 mA per volt squared for power MOSFETs and 100 to 500 mA per volt squared for logic-level MOSFETs. These are effective Kp values that account for the actual device geometry.
What is a logic-level MOSFET?
A logic-level MOSFET has a low Vth (1 to 2 V) and reaches minimum Rds_on at Vgs of 4 to 5 V, enabling direct drive from a 3.3 V or 5 V microcontroller GPIO pin. Standard power MOSFETs require Vgs of 10 V for full enhancement and need a dedicated gate driver IC. Always check the Rds_on specification at the actual Vgs you plan to use. An Rds_on of 10 milliohms at Vgs = 10 V may be 50 milliohms at Vgs = 4.5 V.
How does temperature affect MOSFET threshold voltage?
Threshold voltage decreases by about 2 to 4 mV per degree Celsius for silicon MOSFETs. A device with Vth = 3 V at 25 C may have Vth = 2.4 V at 175 C. This is rarely a problem for switching designs (the gate driver voltage far exceeds Vth in both cases), but it can be significant for circuits that use Vth as a precision voltage reference. The positive temperature coefficient of Rds_on (more resistance when hot) is more commonly the limiting factor in power designs.
How do I calculate the required Vgs for a target drain current?
Rearrange the saturation formula: Vgs = Vth plus square root of (2 times Id divided by Kp). For Id = 100 mA, Vth = 1.5 V, Kp = 50 mA per volt squared: Vgs = 1.5 plus sqrt(2 times 0.1 / 0.05) = 1.5 plus sqrt(4) = 3.5 V. Note that this assumes the device is in saturation, which requires Vds to be at least Vov = Vgs - Vth = 2 V. Use the Find Required Vgs mode of this calculator to compute this directly.
What is transconductance gm and how is it related to Vth?
Transconductance is gm = dId/dVgs = Kp times Vov = sqrt(2 times Kp times Id). It measures how effectively the gate controls the drain current. Higher gm means more voltage gain in an amplifier stage. At Vov = 1 V and Kp = 100 mA per volt squared: gm = 100 mA per volt. At Vov = 3 V: gm = 300 mA per volt. In analog design, gm is set by choosing the bias current and overdrive voltage to meet a gain or bandwidth target.
What is channel-length modulation in a MOSFET?
In reality, drain current in saturation increases slightly with Vds: Id = (Kp / 2) times Vov squared times (1 plus lambda times Vds), where lambda is the channel-length modulation coefficient (typically 0.01 to 0.1 per volt for discrete MOSFETs). This makes the device look like a current source with a finite output resistance Ro = 1 divided by (lambda times Id). This calculator uses the ideal model (lambda = 0), which is accurate for most initial design work and educational purposes.
What is the difference between enhancement-mode and depletion-mode MOSFETs?
An enhancement-mode MOSFET (the most common type) is off at Vgs = 0 and requires a gate voltage above Vth to turn on. A depletion-mode MOSFET has a channel at Vgs = 0 and can be turned off by applying a negative gate voltage. Depletion-mode N-channel MOSFETs have negative Vth (typically -1 to -3 V), meaning they conduct at zero gate bias. They appear in current-source loads, normally-on power switches, and some RF designs. This calculator applies to enhancement-mode devices.
How does W/L ratio affect drain current in a MOSFET?
Drain current scales proportionally with W/L because Kp = mu_n times Cox times W/L. Doubling W/L doubles Kp and doubles the drain current at the same Vgs and Vds. In IC design, W/L is chosen to set the current-carrying capacity of each transistor. For discrete power MOSFETs, the effective W/L is set in manufacturing; its effect is captured in the overall Kp value that can be extracted from the transfer characteristic.