Free engineering calculator

PCR Thermal Cycling Calculator

Size the thermal engine of a PCR cycler: enter the block and sample masses, the ramp rate, and the cycle temperatures, and get the peak heating and cooling power the thermoelectric stack must deliver.

▶  Watch this problem SOLVED - live animated transient

block m_block · wells n × VTEC stackrrT_high 95°T_low 55°C = m₁c_Al + nVρc_w + m_plate c_PPP = C·r ± h_loss (T − T_amb)peak heat @ T_high · peak cool @ T_low

The diagram is labeled with the same symbols as the input fields below.

Watch it solved transiently

Watch YOUR block cycle - and the samples chase it

A live cycling simulation with the heater and cooler powers the calculator just computed: the block chases the 95/55 staircase while the sample liquid visibly lags behind - the lag that hold times exist to absorb.

The full engine

This preview solves a handful of lumped nodes. The NovaThermal engine behind ThermalResults.com (coming soon) runs the same physics on tens of thousands of nodes - full transients with phase change, radiation, fluid loops, and Monte-Carlo design envelopes, GPU-accelerated at 400× real-solver speed - and hands you review-ready margin reports.

The equations this calculator uses

C_total = m_block c_Al + n V ρ c_water + m_plate c_PP   (c_Al = 0.90, c_water = 4.18, c_PP = 1.9 J/g·K)
P_heat = C_total · r + h_loss (T_high - T_ambient)   (worst at T_high)
P_cool = C_total · r - h_loss (T_low - T_ambient)   (worst at T_low)
Assumptions and limits
  • Lumped block: the aluminum block, samples, and plate ramp together at the commanded rate (sample liquid actually lags the block by seconds - see the notes).
  • Specific heats: aluminum 0.90 J/gK, aqueous sample as water 4.18 J/gK, polypropylene consumable 1.9 J/gK - standard handbook values.
  • Surface loss modeled as one linear total conductance (W/K) to ambient; losses HELP the cool-down ramp and FIGHT the heat-up ramp.
  • Peak powers are evaluated at the WORST point of each ramp: heating at T_high (largest loss opposing), cooling at T_low (least loss assisting). Cycle stays above ambient.

Engineering notes

A PCR machine is a precision thermal cycler: 30-40 laps between annealing (~55 °C) and denaturation (~95 °C), as fast and as uniformly as physics allows. The engineering budget is set by one number - the total thermal capacitance C of everything that must swing: the aluminum block dominates, the samples and plastic consumable add their share. Every gram of block metal is power the thermoelectric stack must pump forty times per run.

The asymmetry surprises newcomers: heating is easy (resistive heaters or TEC in heating mode are efficient and overshoot-tolerant), but the COOLING ramp is the sizing case. Pulling C·r watts out of a 95 °C block through thermoelectric modules whose capacity falls with the very temperature difference they must hold is precisely the derate spiral covered in our device-cooling calculator - which is why fast cyclers pair aggressive TEC stacks with serious heat sinks and blowers.

The honest limit of this estimate is uniformity and lag: the liquid inside each well trails the block by several seconds, edge wells run cooler than center wells, and controller overshoot eats into hold accuracy. Those are transient, spatial questions - the natural territory of a full block-and-well network simulation rather than a closed-form balance.

Frequently asked questions

Why does cooling size the thermoelectric stack rather than heating?

Heating can lean on efficient resistive elements or TEC heating mode, but the cool-down ramp must PUMP the block's stored heat out through the modules while they hold a temperature difference - and TEC capacity falls as that difference grows. The peak cooling number is the one to take to module selection.

How fast can a PCR block ramp?

Commercial cyclers span roughly 2-6 C/s block rate. The limit scales as available pumping power divided by total thermal capacitance, so faster machines minimize block mass (thin blocks, fewer wells) as much as they add TEC power.

Do the samples really follow the block temperature?

Not exactly - the liquid lags the block by a time constant of a few seconds that depends on well geometry and volume. Protocol hold times exist partly to let samples catch up. This calculator budgets the power; sample-level lag needs a transient well model.