Temperature in. Voltage out.

Seebeck Calculator

Turn a temperature difference into a voltage — or work backwards from a measured voltage. Covers single thermocouples, multi-couple thermopiles and Bi₂Te₃ modules, with load power and thermoelectric conversion efficiency.

Inputs

Preset material / pair

Preset values fill the coefficient field below — edit freely.

Seebeck coeff. S

Signed. Positive → p-type dominant.

Couples in series (N)

N = 1 single thermocouple; N > 1 thermopile / module.

Hot side T_h

—

Cold / reference T_c

—

Temperature unit

Applies to both temperature fields.

Power & efficiency (optional)

Internal resistance R_int (Ω)

DC resistance of legs + leads. Blank / 0 hides power results.

Load resistance R_load (Ω)

Set equal to R_int for maximum power transfer.

Figure of merit ZT

¯ZT at the mean temperature: ≈0.8–1.1 for cheap modules, 1.5–3 for good ones.

Typical Seebeck coefficients — click a row to use it

Material / pair	S (µV/K)	Basis	Where you meet it
Type E — Chromel / Constantan	+68	whole couple	Highest-output common base-metal thermocouple
Type J — Iron / Constantan	+52	whole couple	Furnaces, older industrial PLCs
Type T — Copper / Constantan	+43	whole couple	Cryogenic & low temperature, food and laboratory
Type K — Chromel / Alumel	+41	whole couple	The workhorse: ovens, engines, kilns, 3D printers
Type N — Nicrosil / Nisil	+33	whole couple	High temperature, lower drift than type K
Type S — Pt / Pt-Rh10%	+6.5	whole couple	Precious metal, up to ~1600 °C, calibration labs
Type B — Pt-Rh30% / Pt-Rh6%	+15	couple, ~1000 °C	Very high temperature; near-zero output at 0 °C
n-type Bi₂Te₃ leg	−215	one leg, 300 K	Peltier coolers & near-room-temperature generators
p-type Bi₂Te₃ leg	+215	one leg, 300 K	Peltier coolers & near-room-temperature generators
Bi₂Te₃ p–n couple	+420	couple (2 legs)	One couple of a TEC / TEG module
n-type PbTe leg	−230	one leg, ~600 K	Mid-temperature waste-heat recovery
p-type SiGe leg	+200	one leg, 300–900 K	Space RTGs, high-temperature staged modules
Constantan vs. copper	−43	relative to Cu	Strain gauges, thermal shunts
PEDOT:PSS (polymer)	−20	one leg, 300 K	Flexible and wearable energy harvesting

Indicative values only. The Seebeck coefficient is strongly temperature dependent (and composition dependent after doping or annealing), so treat these as starting points — use the manufacturer datasheet, or NIST / ITS-90 polynomial tables for anything you must calibrate against.

How it is calculated

Output voltage. V = N · S · (T h − T c). The exact relation is the integral V = N ∫_T c^T h S(T) dT; this page assumes S is constant across the range, so use the value quoted at the mean temperature when the gradient is large.
Sign convention. The result is the potential of the hot-side terminal with respect to the cold-side return. Positive S (p-type) makes the hot side positive, negative S (n-type) makes it negative. Swapping the two wires flips the sign, and reversing the gradient flips it too — both are reflected in the result.
Thermopiles. N identical couples in series add their EMFs, and so do their resistances — hence R int should be the measured DC resistance of the whole device, not of a single leg.
Electrical power. I = V / (R int + R load), P load = I² · R load, and the matched-load maximum P max = V² / (4 · R int).
Efficiency. η = η_Carnot · (√(1+ZT̄) − 1) / (√(1+ZT̄) − T c/T h), with ZT̄ evaluated at (T h + T c)/2. This is the ideal single-pair result: it ignores contact resistance and thermal shorting, so real modules land noticeably below it.
Cold-junction compensation. A thermocouple only senses a difference. To read an absolute temperature you must know T c (the terminal block or interface-IC temperature) and add it: T measured = T c + V / (N · S), which is exactly what the ΔT mode reports.
Open circuit vs. loaded. The EMF computed is the open-circuit voltage. Drawing current pulls the terminal voltage down by I · R int and simultaneously pumps heat back with the Peltier effect, which is why a generator's best operating point is a compromise between voltage and power.