Pumped Hydro Storage Sizing Calculator

Harnessing gravity with pumped hydro

Pumped-storage hydropower (PSH) is the most widely deployed form of large-scale, long-lifetime electricity storage. It works by moving water between two reservoirs at different elevations:

• Charging (pumping): when electricity is cheap/abundant, pumps move water uphill.
• Discharging (generating): when electricity is valuable, water flows downhill through a turbine-generator to produce electricity.

This calculator provides a quick, transparent sizing estimate from four inputs:

• Usable upper-reservoir volume (m³) — the active volume that can actually be cycled (not total reservoir volume).
• Elevation head (m) — the approximate vertical difference between the two water surfaces.
• Round-trip efficiency (%) — combined losses over a full pump→generate cycle.
• Discharge duration (hours) — how long you want the plant to sustain discharge at the implied average power.

What the calculator outputs (and how to read it)

Given your inputs, the tool estimates:

• Gross stored potential energy (before losses), based on gravitational potential energy in the elevated water.
• Deliverable electrical energy (after applying round-trip efficiency), in MWh.
• Average electrical discharge power needed to empty that usable volume over the chosen duration, in MW.
• Average volumetric flow rate required to move that volume over the chosen duration, in m³/s (and often also useful to think of as kg/s via water density).

Important: the power shown is an average over the discharge duration. Real plants have operating ranges (minimum/maximum turbine flow, ramping constraints, and grid dispatch variability), so instantaneous power may differ.

Equations used

The core physics is gravitational potential energy. Using water density ρ ≈ 1000 kg/m³ and gravitational acceleration g ≈ 9.81 m/s²:

1) Gross potential energy (joules):

E_gross = ρ g h V

2) Convert joules to MWh:

1 MWh = 3.6×10⁹ J ⇒ E_gross,MWh = E_gross / (3.6×10⁹)

3) Apply round-trip efficiency to estimate deliverable electrical energy:

E_delivered = E_gross,MWh × η

where η is the round-trip efficiency as a decimal (e.g., 75% → 0.75).

4) Average discharge power over duration T:

P_avg (MW) = E_delivered (MWh) / T (h)

5) Average flow rate to move the usable volume over time:

Q (m³/s) = V (m³) / [T (h) × 3600 (s/h)]

MathML (same relationships, unambiguous formatting)

Note on efficiency terminology: “Round-trip efficiency” normally refers to energy out (electricity generated) divided by energy in (electricity used to pump) over a full cycle. This calculator uses it as a simple derating factor on gross stored potential energy to estimate deliverable electrical energy. That is appropriate for quick sizing, but project studies often separate pumping efficiency, turbine efficiency, generator/motor efficiency, transformer losses, and hydraulic losses.

Worked example

Inputs (matching the default example on the page):

• Usable volume V = 100,000 m³
• Head h = 100 m
• Round-trip efficiency η = 75% = 0.75
• Discharge duration T = 6 h

Step 1 — Gross potential energy:

E_gross = 1000 × 9.81 × 100 × 100000 ≈ 9.81×10¹⁰ J

E_gross,MWh ≈ (9.81×10¹⁰) / (3.6×10⁹) ≈ 27.25 MWh

Step 2 — Deliverable electrical energy:

E_delivered ≈ 27.25 × 0.75 ≈ 20.44 MWh

Step 3 — Average discharge power over 6 hours:

P_avg ≈ 20.44 / 6 ≈ 3.41 MW

Step 4 — Average flow rate:

Q ≈ 100000 / (6 × 3600) ≈ 4.63 m³/s

That flow corresponds to a mass flow of ṁ = ρQ ≈ 1000 × 4.63 ≈ 4630 kg/s.

Comparison table: how inputs move the outputs

The relationships are linear in volume and head, and linear in efficiency for deliverable energy and power. Duration only affects power and flow (not total energy).

Interpreting results in practice

• Energy (MWh) tells you how much electrical energy you can approximately deliver per full discharge of the usable volume. If you need a target energy (e.g., 200 MWh), you can iterate on volume/head/efficiency to see what combinations reach it.
• Power (MW) indicates the average output for the chosen duration. Real projects often choose turbine capacity based on market needs (e.g., 4-hour vs 10-hour storage), grid interconnection limits, and waterway constraints.
• Flow (m³/s) is a key driver of penstock diameter, valve sizing, and hydraulic losses. If the implied flow seems impractically large, you can increase head (more energy per unit volume) or increase duration (lower flow for the same volume).

Assumptions & limitations (read before using for design)

• Constant head assumption: the calculator assumes the head h is constant. In reality, reservoir water levels change during charge/discharge, so effective head varies over time.
• No hydraulic loss model: penstock friction, bends, valves, trash racks, and draft tube losses are not modeled. These reduce net head and therefore reduce delivered energy/power compared to the idealized ρghV estimate.
• Efficiency treated as a single factor: round-trip efficiency is applied as one combined multiplier. Real systems have separate pump, turbine, motor/generator, transformer, and variable-speed losses, which also vary with flow and head.
• Usable volume must be realistic: “usable” means the active storage between operating levels. Dead storage, minimum ecological releases, sediment allowance, and freeboard are not included unless you subtract them yourself.
• Average (not peak) power: the computed MW is the average needed to empty the usable volume over the duration. Turbine nameplate capacity, ramp rates, and minimum stable generation are not addressed.
• Water availability and constraints not included: seasonal inflows, evaporation, seepage, water rights, and environmental permitting can dominate feasibility and are outside the scope here.
• Not a substitute for engineering design: treat results as screening-level. Preliminary design typically adds a hydraulic model, operating strategy, equipment curves, and civil/geotechnical constraints.

If you want a quick sanity check: typical round-trip efficiency values are often in the ~65–85% range depending on equipment and operating conditions, and practical heads vary widely (from tens of meters to several hundred meters). Use your site-specific data whenever possible.