Renewables calculators.Heat pumps, solar PV, batteries, solar thermal and EV-ready energy maths.

Heat loss

Heat lossRoom design heat loss (fabric U·A·ΔT plus ventilation 0.33·n·V·ΔT)

Δ T = T_{i} - T_{e}

Heat lossWhole-house design heat loss and W/m²

P = P_{1} + P_{2} + P_{3} + P_{4} + P_{5} + P_{6} + P_{7} + P_{8}

Heat lossIndicative heat loss from EPC heating demand (MCS 031 method)

P_{s} = \frac{1000 Q}{24 D}

Heat pump selection

Heat pump selectionHeat pump capacity check against design heat loss (MIS 3005-D)

P_{r e q} = P_{d} (1 + \frac{m}{100})

Emitters

EmittersRadiator output at heat pump flow temperatures (ΔT correction)

Δ T = \frac{T_{f} + T_{r}}{2} - T_{i}

EmittersRequired radiator size (ΔT 50 rating) and oversize factor for a heat pump

Δ T = \frac{T_{f} + T_{r}}{2} - T_{i}

Hydraulics

HydraulicsPrimary flow rate from heat output and temperature difference (Q = ṁ·cp·ΔT)

\dot{m} = \frac{P}{c_{p} Δ T}

HydraulicsPipe velocity check and heat-carrying capacity

A = \frac{π (d / 1000)^{2}}{4}

HydraulicsMinimum system volume and buffer or volumiser size

V_{r e q} = \max (V_{m}, r P)

Energy and running costs

Energy and running costsAnnual heat demand from design heat loss and degree days

H = \frac{P_{d}}{T_{i} - T_{e}}

Energy and running costsAnnual running cost: heat pump compared with a gas boiler

E_{h p} = \frac{Q}{S}

Energy and running costsAnnual carbon saving: heat pump compared with a gas boiler

G_{h p} = \frac{Q}{S} f_{e}

Planning and grants

Planning and grantsHeat pump sound level at the assessment position (MCS 020 method)

L_{p} = L_{w} + 10 \log_{10} (\frac{Q}{4 π r^{2}}) - B

Planning and grantsBoiler Upgrade Scheme grant and customer contribution (England and Wales, from 21 July 2026)

C_{c} = \max (0, C - G)

Hot water

Hot waterHot water cylinder reheat time

E = \frac{V ρ c_{p} (T_{2} - T_{1})}{3600}

Yield and sizing

Yield and sizingPV annual yield estimate (MCS method)

E = P_{pk} K_{k} S_{F}

Yield and sizingArray size from panel count

P_{pk} = \frac{N W_{p}}{1000}

Yield and sizingNumber of panels that fit a roof (portrait)

n_{c} = ⌊ \frac{1000 W_{r} - 2 e + s}{B + s} ⌋

Yield and sizingTilt and orientation loss (Kk comparison)

L_{p} = 100 (1 - \frac{K_{a}}{K_{o}})

String design

String designCold open-circuit string voltage and maximum modules per string

V_{c} = V_{o c} (1 + \frac{β_{V}}{100} (T_{\min} - 25))

String designMinimum modules per string (hot Vmp vs MPPT minimum)

T_{c} = T_{a} + \frac{(NOCT - 20) G}{800}

DC cabling

DC cablingString design current and DC cable rating check (1.25 × Isc)

I_{b} = 1.25 I_{s c} N_{p}

DC cablingDC string cable voltage drop

R_{t} = R_{20} (1 + 0.00393 (θ - 20))

Inverter and grid connection

Inverter and grid connectionInverter sizing ratio (DC/AC)

R = \frac{P_{d c}}{P_{a c}}

Inverter and grid connectionG98 limit check (16 A per phase)

P = P_{p v} + P_{b}

Self-consumption and payback

Self-consumption and paybackSelf-consumption and export estimate

E_{s c} = \frac{E f}{100}

Self-consumption and paybackSimple payback from bill savings and SEG export

S_{s c} = \frac{E f}{100} \frac{p_{i}}{100}

Batteries

BatteriesBattery usable capacity

E_{u} = \frac{C_{n} DoD}{100}

BatteriesBattery autonomy (hours of supply)

t = \frac{E_{u} (1 - r / 100)}{P}

Solar thermal

Solar thermalSolar thermal collector output (ISO 9806 / EN 12975 efficiency curve)

Δ T = T_{m} - T_{a}

EV charging

EV chargingEV charging time from charger power and efficiency

E_{b} = \frac{C_{b} (S_{2} - S_{1})}{100}

Carbon

CarbonCO₂e saving from solar generation (UK grid factor)

M = E \times EF

Renewables calculators.Heat pumps, solar PV, batteries, solar thermal and EV-ready energy maths.

Heat loss

Heat pump selection

Emitters

Hydraulics

Energy and running costs

Planning and grants

Hot water

Yield and sizing

String design

DC cabling

Inverter and grid connection

Self-consumption and payback

Batteries

Solar thermal

EV charging

Carbon

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