# Pump Calculator

Pump calculator figures hydraulic HP, brake HP, motor HP, and kW draw from flow rate, total dynamic head, specific gravity, and pump efficiency. Hydraulic Institute formulas.

## What this calculates

This pump calculator returns hydraulic horsepower, brake horsepower at the pump shaft, required motor horsepower with service factor, and the next standard NEMA motor size. It uses the Hydraulic Institute formula HP = Q x H x SG / 3960 for any centrifugal or positive-displacement pump moving water, seawater, fuel, brine, or sludge. Use it to size a booster pump, pool pump, transfer pump, sump pump, or irrigation pump.

## Inputs

- **Flow Rate** (gpm) — min 0 — Design flow rate the pump must deliver
- **Total Dynamic Head** (ft) — min 0 — Sum of static lift + elevation + friction + pressure (1 psi = 2.31 ft)
- **Specific Gravity of Fluid** — options: Water (1.00), Seawater (1.03), Brine / 20% salt (1.20), Diesel fuel (0.85), Gasoline (0.72), Light crude oil (0.92), Sludge 30% solids (1.30), Sulfuric acid 98% (1.84) — Specific gravity adjusts horsepower for non-water fluids
- **Pump Efficiency** (%) — min 30, max 90 — Centrifugal 60-80%, positive displacement 80-90%, submersible 55-70%
- **Motor Efficiency** (%) — min 60, max 98 — NEMA Premium motors 92-96%, standard motors 84-90%
- **Motor Service Factor** — options: 1.00 (no extra capacity, TEFC sealed), 1.15 (NEMA standard open-drip-proof, typical), 1.25 (heavy-duty applications) — Service factor lets motor briefly exceed nameplate HP

## Outputs

- **Hydraulic Horsepower** (HP) — Theoretical power transferred to fluid: Q x H x SG / 3960
- **Brake Horsepower (BHP)** (HP) — Shaft power input required at the pump shaft
- **Required Motor HP** (HP) — Electric motor HP needed accounting for motor efficiency and service factor
- **Standard Motor Size** (HP) — Next standard NEMA motor size to specify
- **Electrical Input Power** (kW) — Actual power the motor draws from the grid
- **Total Head (metric)** (m)
- **Discharge Pressure** (psi) — Assuming no residual suction pressure

## Details

## Pump Calculator Formula

The core equation from the Hydraulic Institute pump engineering handbook:

**Hydraulic HP = Q x H x SG / 3960**

Where:

- **Q** = flow rate in gpm (US gallons per minute)
- **H** = total dynamic head in feet
- **SG** = specific gravity of the fluid (water = 1.00)
- **3960** = conversion constant

Hydraulic HP is the theoretical power transferred to the fluid. Real pumps are 50-85% efficient, so you need more shaft power than the hydraulic HP.

## From Hydraulic HP to Brake HP to Motor HP

**Brake HP (BHP) = Hydraulic HP / pump efficiency**

BHP is the shaft power the pump actually needs. A 10 HP hydraulic load on a 70% efficient pump needs 14.3 HP at the shaft.

**Motor HP = Brake HP / service factor**

NEMA standard service factor on open-drip-proof motors is 1.15, meaning the motor can run 15% over nameplate briefly. A 14.3 BHP load can use a 12.4 HP motor (14.3 / 1.15) but the next standard size is 15 HP.

## Common Pump Efficiencies

| Pump Type | Typical Efficiency |
|-----------|-------------------|
| End-suction centrifugal | 65-80% |
| Multi-stage centrifugal | 60-75% |
| Submersible well pump | 55-70% |
| Sump pump (small residential) | 40-55% |
| Pool circulation pump | 60-70% |
| Positive displacement (gear, piston, diaphragm) | 80-90% |
| Progressive cavity | 70-80% |

Lower efficiency means more brake HP for the same hydraulic output. Submersibles have lower efficiency because motor cooling losses and the confined geometry hurt performance.

## Specific Gravity Adjustment

Specific gravity (SG) scales the horsepower proportionally. Seawater (SG 1.03) needs 3% more HP than freshwater. 30% solids sludge (SG 1.30) needs 30% more HP. Sulfuric acid 98% (SG 1.84) nearly doubles the required HP vs water.

| Fluid | SG |
|-------|----|
| Water | 1.00 |
| Seawater | 1.03 |
| Brine (20% salt) | 1.20 |
| Milk | 1.03 |
| Diesel fuel | 0.85 |
| Gasoline | 0.72 |
| Sludge 30% solids | 1.30 |
| Sulfuric acid 98% | 1.84 |

## Total Dynamic Head

Total dynamic head (TDH) is the total "lift" work the pump must do:

- **Static lift** = vertical height from source water level to discharge
- **Friction losses** in the pipe (Hazen-Williams or Darcy-Weisbach)
- **Pressure head** at the discharge (1 psi = 2.31 ft of water head)
- **Elevation change** from start to end
- **Velocity head** (usually small, often ignored)

Example: A pump moves 100 gpm from a lake 20 ft below grade to a tank 50 ft above grade, through 500 ft of 4-inch pipe, delivering 30 psi at the tank.

- Static lift: 20 ft
- Elevation rise: 50 ft
- Friction loss at 100 gpm in 4" pipe: 1.5 ft per 100 ft x 5 = 7.5 ft
- Pressure head: 30 psi x 2.31 = 69.3 ft
- **Total TDH = 146.8 ft**

At 100 gpm and 147 ft TDH moving water at 70% pump efficiency: hydraulic HP = 100 x 147 / 3960 = 3.71 HP. BHP = 3.71 / 0.70 = 5.3 HP. With a 1.15 service factor (motor can run 15 percent above nameplate), required motor HP = 5.3 / 1.15 = 4.6. Standard motor: **5 HP** (next NEMA size up from 4.6).

## When to Oversize

- High-viscosity fluid: add 20% to HP
- Frequent startups: add 10-15%
- Long pipe runs with valves and elbows: verify friction loss calculation
- Future capacity: one size up if expansion is likely

## When NOT to Oversize

- Oversized pumps run "off the curve" at low efficiency, waste energy, and destroy seals and impellers via cavitation.
- A 7.5 HP motor on a 3 HP pump load runs the motor at 40% load, poor efficiency (85% vs 92% at full load), and the larger contactor cycles more.
- Right-size the pump first, then size the motor for that pump at the actual operating point.

## Pump Calculator Examples

**Pool pump:** 50 gpm, 30 ft TDH, water, 65% efficiency = 0.38 hydraulic HP, 0.58 BHP. Standard: **3/4 HP single-speed** or **1.5 HP variable-speed** (VS pumps save 60-80% on energy).

**Irrigation pump:** 150 gpm, 80 ft TDH, water, 70% efficiency = 3.0 hydraulic HP, 4.3 BHP. Standard: **5 HP**.

**Transfer pump (diesel fuel):** 100 gpm, 50 ft TDH, SG 0.85, 75% efficiency = 1.07 hydraulic HP, 1.43 BHP. Standard: **2 HP**.

**Municipal booster pump:** 500 gpm, 120 ft TDH, water, 80% efficiency = 15.2 hydraulic HP, 19 BHP. Standard: **20 HP**.

## Frequently Asked Questions

**Q: What formula does the pump calculator use?**

A: It uses the Hydraulic Institute formula HP = Q x H x SG / 3960, where Q is flow in gpm, H is total dynamic head in feet, SG is specific gravity, and 3960 is the conversion constant. The result is hydraulic horsepower. The calculator then divides by pump efficiency to get brake HP and applies the motor service factor to select the next standard NEMA motor size.

**Q: How do I figure total dynamic head for a pump?**

A: TDH = static lift + elevation rise + friction losses + pressure head. Static lift is the vertical distance from water source to discharge. Friction loss is about 1.5 ft per 100 ft of 4-inch pipe at 100 gpm (more for smaller pipe). Pressure head converts at 1 psi = 2.31 ft. A pump moving 100 gpm up 70 ft with 30 psi discharge through 500 ft of 4-inch pipe has a TDH of about 147 ft.

**Q: What is brake horsepower (BHP) for a pump?**

A: Brake horsepower is the shaft power the pump actually needs, accounting for internal losses. BHP = hydraulic HP / pump efficiency. A 10 hydraulic HP load on a pump that is 70% efficient requires 14.3 BHP at the shaft. The motor must deliver at least that much (typically with a 1.15 service factor cushion, so a 12.5 HP motor can handle a 14.3 BHP load briefly).

**Q: Why does specific gravity matter in the pump HP calculation?**

A: Specific gravity scales horsepower proportionally because heavier fluids take more energy to lift and push. Seawater (SG 1.03) needs 3% more HP than freshwater at the same flow and head. Brine (SG 1.20) needs 20% more. 98% sulfuric acid (SG 1.84) nearly doubles the HP. Always adjust SG when pumping anything other than plain water.

**Q: What efficiency should I use for a centrifugal pump?**

A: Typical centrifugal pump efficiency ranges from 55-80% depending on type. End-suction centrifugals average 65-80%. Multi-stage centrifugals 60-75%. Submersibles 55-70%. Small sump pumps 40-55%. If the pump manufacturer publishes a curve, use the efficiency at your operating point. If unknown, 70% is a reasonable default for industrial centrifugals.

**Q: How do I convert pump head in feet to psi?**

A: For water: 1 psi = 2.31 ft of head. So 100 ft of head = 43.3 psi. For other fluids, divide by specific gravity as well. 100 ft of head moving SG 1.20 brine = (100 / 2.31) x 1.20 = 52 psi at the pump discharge. The calculator handles these conversions automatically based on the specific gravity you select.

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Source: https://vastcalc.com/calculators/construction/pump
Category: Construction
Last updated: 2026-04-08