# Drag Force Calculator (F_D = ½·ρ·v²·C_D·A)

Compute the drag force on a body in a fluid stream: F_D = ½·ρ·v²·C_D·A (N), where ρ is the fluid density, v the free-stream velocity, C_D the drag coefficient (shape- and Reynolds-dependent), and A the reference (frontal projected) area. A built-in shape library supplies typical high-Re C_D values: sphere 0.47, hemisphere 0.42, long cylinder 0.81, disk/flat plate 1.17, cube 1.05, streamlined airfoil 0.04, long streamlined ellipsoid 0.07, cone 0.50; or choose 'Custom' to enter C_D directly. Optionally, with dynamic viscosity μ and characteristic length L, the Reynolds number Re = ρ·v·L/μ is computed, and the power dissipated by drag P = F_D·v (W). Density in kg/m³/g/cm³, velocity in m/s/km/h, area in m²/cm²/mm², length in m/cm/mm.

> Canonical page: https://elysiatools.com/en/tools/drag-force-calculator

- **Category:** Math & Numbers

- **Keywords:** drag force, drag coefficient, Cd, bluff body, streamlined body, Reynolds number, fluid mechanics, aerodynamic drag, hydrodynamic drag, frontal area

## Overview

Calculate the drag force on a body in a fluid stream using F_D = ½·ρ·v²·C_D·A. Enter fluid density, velocity, drag coefficient, and frontal reference area to get force in newtons, plus drag power in watts. Add dynamic viscosity and characteristic length to calculate the Reynolds number.

## Inputs

- **Shape** (select): Body shape. Selecting a preset fills the typical drag coefficient C_D for that shape at high Reynolds number. Choose 'Custom' to enter C_D directly.
- **Drag Coefficient C_D** (number): Drag coefficient C_D (0 to 5). When a preset Shape is selected, the typical value is filled in automatically; you may still override it. Choose Shape = Custom to enter your own value.
- **Fluid Density ρ** (number): Fluid density ρ. Enter in the selected Density Unit.
- **Density Unit** (select)
- **Free-stream Velocity v** (number): Free-stream velocity v. Enter in the selected Velocity Unit.
- **Velocity Unit** (select)
- **Reference (Frontal) Area A** (number): Reference (frontal projected) area A. Enter in the selected Area Unit.
- **Area Unit** (select)
- **Dynamic Viscosity μ (optional, for Re)** (number): Dynamic viscosity μ of the fluid in Pa·s. Optional — when supplied together with a characteristic length L, the Reynolds number Re = ρ·v·L/μ is computed.
- **Characteristic Length L (optional, for Re)** (number): Characteristic length L of the body. Optional — used only to compute Re. Enter in the selected Length Unit.
- **Length Unit** (select)
- **Decimal Places** (number)

## When to use

- Estimate aerodynamic drag on objects moving through air.
- Calculate hydrodynamic drag on bodies in water or another fluid.
- Compare the effect of shape, velocity, density, or frontal area on drag force.

## How it works

- Choose a preset shape to use its typical high-Reynolds-number drag coefficient, or select Custom and enter C_D directly.
- Enter fluid density, free-stream velocity, and frontal reference area, selecting the appropriate units.
- The calculator converts the inputs and applies F_D = ½·ρ·v²·C_D·A to return drag force in newtons.
- Optionally enter dynamic viscosity and characteristic length to calculate Re = ρ·v·L/μ; drag power is also calculated as P = F_D·v.

## Use cases

- Aerodynamic estimates for vehicles, spheres, airfoils, and other bodies in air.
- Hydrodynamic calculations for submerged objects moving through water.
- Early-stage fluid mechanics comparisons using different shapes and reference areas.

## Frequently asked questions

### What formula does the calculator use?

It uses F_D = ½·ρ·v²·C_D·A, where ρ is density, v is velocity, C_D is drag coefficient, and A is frontal reference area.

### What units are supported?

Density supports kg/m³ and g/cm³; velocity supports m/s and km/h; area supports m², cm², and mm²; length supports m, cm, and mm.

### Can I enter my own drag coefficient?

Yes. Choose Custom or override a preset value, then enter C_D directly.

### How is the Reynolds number calculated?

When dynamic viscosity and characteristic length are provided, Re is calculated as ρ·v·L/μ.

### What additional result is provided?

The calculator also reports power dissipated by drag using P = F_D·v, in watts.

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