What this calculator works out
This calculator applies the standard free-fall equations to give the speed and time for an object dropped from a given height, with no air resistance.
It is included as a physics reference point. Real blood droplets do not follow it, because air resistance becomes significant almost immediately for something that small. This is a teaching aid, not a casework tool.
Fall height
Before you apply the result
- The equations assume a vacuum. For a blood droplet in air the difference is substantial after even a short fall.
- Height is in metres and gravity in metres per second squared. The default is standard gravity.
- The result describes an object released from rest. A droplet projected with initial velocity behaves differently.
- Droplets also break up, oscillate and reach terminal velocity — none of which this models.
A blood droplet falling in air accelerates until drag balances gravity, then stops accelerating. For typical droplet sizes this terminal velocity is in the region of 5 to 7 metres per second and is approached within a few metres of fall. Free-fall equations exceed it and keep rising, which is where they part company with reality.
How this calculator works
The standard constant-acceleration equations:
Impact speed = √(2 × g × height)
Fall time = √(2 × height ÷ g)Both follow from constant acceleration with zero initial velocity. Speed rises with the square root of height, so doubling the drop height increases impact speed by only about 41%.
Introducing air resistance changes the shape entirely: speed rises quickly at first, then flattens towards terminal velocity. Beyond a few metres the free-fall figure is simply wrong for a droplet.
Worked example: a one metre fall
Using the default figures — 1 metre, standard gravity of 9.80665 m/s²:
- Impact speed: 4.429 m/s
- Fall time: 0.452 seconds
At one metre the free-fall figure is still in the right region, because the droplet has not yet approached terminal velocity. At ten metres free fall predicts 14.0 m/s, while a real blood droplet would be travelling at roughly half that and would have stopped accelerating some metres earlier. The equations are useful for the first metre or two and misleading beyond.
Common mistakes
- Applying free-fall speeds to long drops. Air resistance dominates well before that.
- Assuming a droplet stays intact. Larger droplets oscillate and can break up in flight.
- Ignoring initial velocity. A projected droplet does not start from rest.
- Reading a stain size back to a fall height. Too many variables intervene.
- Using a non-standard gravity value without reason. It varies by well under a tenth of a percent across the UK.
Frequently asked questions
What is the terminal velocity of a blood droplet?
It depends on droplet size, but for typical volumes it is broadly in the range of 5 to 7 metres per second, reached after a fall of a few metres. Larger droplets have a higher terminal velocity because their mass rises faster than their cross-sectional area. This is why free-fall equations diverge from reality so quickly.
Can fall height be determined from a stain?
Not reliably. Stain diameter increases with impact velocity, and velocity increases with height up to terminal velocity — but the relationship also depends on droplet volume and the surface, and it saturates once terminal velocity is reached. Above a few metres, stains from different heights are effectively indistinguishable.
Why include this if it does not apply?
Because understanding what the idealised physics predicts is what makes the departure from it meaningful. A student who has seen free fall predict 14 m/s at ten metres, and then learns that the droplet is travelling at half that and stopped accelerating long before, understands terminal velocity in a way that a definition does not convey.
Does droplet size affect fall time in a vacuum?
No. In the absence of air resistance all objects fall at the same rate regardless of mass — the classic result. It is precisely air resistance that makes size matter, and blood droplets are small enough that it matters a great deal.
Is what I enter stored?
No. Values are processed entirely in your browser and never transmitted or retained.
Related tools
References
- GOV.UK — Forensic Science Regulator guidance on scientific method and validation
- Met Office — environmental conditions affecting outdoor scene interpretation
Sources are checked at publication and can change — how I choose and check references.