EV Range and Energy Consumption Calculator

Longitudinal energy balance

This is a backward energy calculation, using the force terms in Iora & Tribioli (2019), attached source s2, p. 3, Eq. (1). For each interval the distance is $\Delta s=\bar v\Delta t$ and wheel work is

Positive wind is a headwind. The signed aerodynamic term also handles a tailwind faster than the car. The road angle satisfies $\sin\theta=\Delta h/L$ because L is road distance. Effective rotating mass affects kinetic energy only.

Battery traction power is $P_d=\max(P_w,0)/\eta_d$. Available generator DC power is $P_a=\min(\max(-P_w,0)\eta_r,P_{g,max})$. Let $P_s$ be HVAC plus base accessory demand. Accepted recovery at the DC bus is $P_r=\min(P_a,P_s+P_{chg,max})$, giving net battery power $P_b=P_d+P_s-P_r$. The battery charging cap therefore applies after accessories, while a separate generator cap limits total recovered electrical power. Recovered energy at the DC bus includes both accessory supply and battery charging; net energy into the battery during braking is reported separately. Regeneration acts on total negative wheel power, after road resistance; it is never credited against the full kinetic-energy loss independently. Summing interval power times duration gives DC-terminal energy. Endpoint kinetic energy is exact per interval; drag uses interval mean speed.

Driving patterns and range

Steady mode has constant speed without launch or parking. EPA UDDS and HWFET retain every official one-second sample (attached s4/s5); interval means preserve the speed-trace integral. Their per-cycle consumption is scaled by trip distance, including a fractional average final cycle. These are exploratory energy estimates, not certification tests or WLTP results. Current capacity is usable capacity times availability. Range is energy between starting charge and reserve divided by consumption. For nonpositive net discharge, only the depletion-range value is unavailable (shown as a dash); trip energy, regeneration, time and valid arrival charge remain visible.

Temperature and HVAC

Dry-air density is $p/(R T)$, with $R=287.05$ J/(kg·K). Pressure stays constant; use local absolute pressure. Celsius degree increments are bridged explicitly to kelvin. Outdoor Fahrenheit input is converted by the usual offset equation. Heating and cooling use adjustable electrical W/K slopes, separate thresholds and caps. With the defaults, heating below 20 °C adds 5800/35 W per kelvin, capped at 5800 W, plus 200 W base accessories. This reproduces the winter auxiliary model in s2, p. 6. Cooling defaults are illustrative. Manual mode accepts measured HVAC electrical power.

Independent comparisons

DOE/INL Leaf reference cases compare measured mean battery power at 45 and 60 mph and ANL UDDS/HWFET consumption (s3, pp. 2–3). These use total test mass 3927 lb = delivered 3595 lb plus 332 lb, with explicit approximate Leaf parameters from the modelling literature: Cd 0.28, A 2.3 m², Crr 0.012, traction efficiency 80%, base 200 W and effective regeneration 65%. These are declared modelling assumptions, not fitted coefficients or a validated Leaf preset. Allowances are ±15% for steady/highway cases and ±20% for city driving; the UDDS prediction is about 17% high and HWFET about 7% high. The HVAC reference checks are exact tests of a published correlation, not vehicle measurements.

The DOE constant-speed table's stated DC Wh/mi does not consistently follow its listed charge-energy row. Battery output energy divided by distance also differs from charge-input consumption. Accordingly, the constant-speed checks use the independently stated mean DC power row, without changing the equations to fit the inconsistent consumption entries.

• Default vehicle: an illustrative 60 kWh usable, 1800 kg loaded passenger EV; these numbers do not identify an OEM model. Vehicle inputs are editable.
• Newtonian rolling, aerodynamic, gravity and kinetic-energy equations are applied here. Air is dry; gravity is 9.80665 m/s². No fitted range correction is used.
• The full journey has one uniform grade, constant wind, pressure and ambient temperature. Elevation is destination minus start, not cumulative climbing. Range repeats that grade and driving pattern.
• Traction and regeneration efficiencies are constant effective values. Total generator DC output and net battery charging power have separate caps. The illustrative default generator limit is 100 kW; the battery cap applies after accessories. Unaccepted wheel braking energy is absorbed by friction brakes. Cold/full-pack restrictions are entered through the battery charging cap and recovery settings; there is no automatic SOC-dependent controller.
• Capacity availability represents temperature and ageing together; it scales usable energy once. Battery voltage, internal resistance, state-dependent capacity and thermal transients are excluded. The model stops at the user's reserve; manufacturer buffers are already excluded from usable capacity.
• HVAC is a steady electrical load. Its winter default follows s2; cooling slope, heating/cooling caps and thresholds are adjustable assumptions. There is no cabin warm-up, sunshine, humidity, defrost, COP map or battery-conditioning model. When a cap is reached, cabin comfort is not guaranteed.
• EPA speed traces are prescribed exactly as published. Wheel-power warnings do not derate speed. Cycle scaling is statistical, so it does not claim to track an arbitrary partial cycle.
• The schematic uses explicitly labelled metric units. Charts use their labelled axis units. The catalog SI/US switch converts supported physical input/result units; Wh/km and Wh/mi are both provided. Outdoor temperature has its own Celsius/Fahrenheit selector.

Use for first-order passenger-EV comparisons on firm roads, 5–160 km/h steady speed, −30 to +45 °C, and uniform road slopes up to about 15% rise per road distance. This is not a navigation, certification, braking-distance or battery-safety tool. The sweep spans 10–160 km/h; its 20 °C and −10 °C curves retain the selected capacity availability, HVAC mode and route. Turning HVAC off also turns it off for comparison curves. Selected-temperature predictions are plotted as points every 10 km/h over the continuous 20 °C and −10 °C curves; coincident points remain visible above a comparison line.

For rolling hills, calculate each climb/descent separately. A constant net descent can return energy, so it has no finite battery-depletion range; the range card shows a dash while trip energy and valid arrival charge remain visible. Net recovered energy is negative battery consumption, not zero range. A prediction above 100% charge is invalid: lower starting charge or the net charging cap; for a battery that fills mid-descent, split the leg and set the charging cap to zero after it fills. Gaps in speed-range curves likewise mark nonpositive consumption. Near-full packs may accept much less charging power: reduce the net battery charging cap using vehicle data. At a zero charging cap, regeneration can still power accessories, subject to the generator limit. The power-cap and cabin-load warnings flag conditions that a prescribed trace cannot resolve.

Use DC-terminal measurements when comparing consumption; wall-plug charging losses are excluded. The approximate Leaf benchmark tolerances expose model uncertainty rather than guarantee accuracy for another vehicle. City-cycle energy is especially sensitive to power-dependent efficiency and brake blending. No BMW i3 dataset was imported or claimed as validation. Keep a journey margin and check predictions against your own car and conditions.