BJT Beta (Gain) Calculator
Calculate transistor beta (β or hFE) using collector and base current values. Useful for BJT amplifier design, biasing, and current-gain analysis.
What the BJT beta calculator does
The BJT beta calculator divides collector current by base current to give the DC current gain of a bipolar junction transistor, written β or hFE. Enter the two currents in the same unit, milliamps or amps, and press Calculate. The result is a dimensionless ratio.
The formula
β = IC / IB
With the default values, 10 mA collector current and 0.1 mA base current, β = 100. The related quantity alpha, the ratio of collector to emitter current, is α = β / (β + 1) = 0.990 for that transistor, and the emitter current is IE = IC + IB = 10.1 mA.
Worked examples
| Transistor | IC | IB | β |
|---|---|---|---|
| Small-signal, e.g. 2N3904 | 10 mA | 60 µA | 167 |
| High-gain, e.g. BC549C | 2 mA | 4 µA | 500 |
| Power, e.g. TIP31 | 1 A | 25 mA | 40 |
| Darlington, e.g. TIP120 | 3 A | 1 mA | 3,000 |
Enter 1 and 0.025 for the power transistor, or 1000 and 25 in milliamps; either way the ratio is 40.
Measuring β on the bench
- Build a simple common-emitter circuit: a base resistor from a supply to the base, a collector resistor to the supply, emitter to ground.
- Measure the voltage across the base resistor and divide by its value to get IB.
- Measure the voltage across the collector resistor and divide by its value to get IC. Make sure the transistor is not saturated: VCE should be well above 1 V.
- Enter the two currents.
Multimeters with an hFE socket do the same test at a fixed base current, typically 10 µA, which is why their readings differ from datasheet values taken at other currents.
Why β is not a constant
- Part-to-part spread. A 2N3904 is specified for hFE between 100 and 300 at 10 mA. Manufacturers sort some families into gain groups (A, B, C).
- Collector current. Gain peaks at a few milliamps for small transistors and falls at both very low and very high currents.
- Temperature. β rises roughly 0.5% per °C, so a hot transistor has more gain.
- VCE. Gain increases slightly with collector voltage (the Early effect) and collapses in saturation.
Good circuits are designed so that their operating point does not depend on the exact β, as the BJT biasing network calculator shows.
DC beta versus AC beta
hFE is the DC ratio of total currents. The small-signal gain hfe, with a lower-case subscript, is the ratio of a small change in IC to the change in IB that caused it. The two are close in the middle of the operating range but diverge at the extremes. Datasheets list both; this calculator gives hFE.
Using β in design
To switch a 200 mA relay coil with a transistor whose minimum β is 50, the base needs at least 200 / 50 = 4 mA. Designers use two to five times that, an “overdrive” that guarantees saturation across temperature and part variation. From a 5 V logic output through a base resistor with 0.7 V across the junction, a 10 mA base drive needs (5 − 0.7) / 0.010 = 430 Ω. In amplifiers the same ratio sets input impedance: the base looks like β × (re + RE), so higher gain means a lighter load on the previous stage.
Common mistakes
- Mixing units. IC in milliamps with IB in microamps gives a result 1,000 times too small.
- Measuring in saturation. When VCE is near 0.2 V, extra base current no longer increases IC, and the calculated β is meaningless.
- Designing for typical β. Use the datasheet minimum for switching circuits and assume the maximum when checking for saturation in amplifiers.
- Treating a Darlington like a single transistor. Its β is the product of two gains and its VBE is about 1.4 V.
Related tools
The voltage divider and current divider calculators handle the resistor networks around the transistor. The power dissipation calculator checks collector and base resistor ratings, and the RC low-pass filter calculator sets the bandwidth of a stage.
External references
Frequently asked questions
What is a typical beta?
100 to 300 for small-signal transistors, 20 to 100 for power transistors, and 1,000 or more for Darlington pairs.
Is a higher beta always better?
Not necessarily. High-gain parts have lower voltage ratings and their gain is less predictable. For switching, enough base drive matters more than the exact figure.
How do I convert beta to alpha?
α = β / (β + 1). For β = 100, α = 0.990. Alpha is the fraction of emitter current that reaches the collector.
Why does my meter read a different beta from the datasheet?
The meter tests at one fixed base current and room temperature. Datasheets quote gain at specific collector currents and voltages, which differ from the meter’s conditions.
Does this work for MOSFETs?
No. MOSFETs are voltage-controlled and have no base current; their equivalent parameter is transconductance.