DEVICE × DRUG

Injection performance

Explore delivery force, time and formulation limits together. Calculations run in this browser without sending these inputs to AI. Save locally only when you choose.

YOUR CALCULATION JOURNEY

From inputs to injection insight

Follow the steps. Review example values before treating the calculation as your project.

0 / 3steps reviewed

● Teal: reviewed● Blue: next step● Red: missing / invalid● Amber: assumption

1Your next step
Dose & target
Choose volume, or dose ÷ concentration. Set the delivery-time target.
Open inputs → I reviewed these inputs
2To review
Drug properties
Enter viscosity at the operating temperature, or apply a fitted curve.
Open inputs → I reviewed these inputs
3To review
Device & assumptions
Enter geometry and force. Review glide-force and outlet-pressure evidence.
Open inputs → I reviewed these inputs

Next: Dose & target

Open the inputs, replace or accept the example values, then mark this step reviewed.

Go to next step →

● Calculation available○ Review incomplete — results may still use examples◆ Assumed inputs in use

Input review is a checklist, not validation of the product. Editing calculation inputs resets the review checklist. Results continue to update automatically.

Which inputs are required, and which can use estimates?

Input	What you need to provide	What the system can do / basis
Volume or dose + concentration Required	Volume in mL, or both dose in mg and concentration in mg/mL.	Calculates volume = dose ÷ concentration. It does not estimate a therapeutic dose.
Viscosity and temperature Required	Viscosity at the intended temperature, or suitable measured data points.	Interpolates a supplied curve or fits empirical models to your measurements. Automatic selection compares prediction errors by leaving out each measured condition. Predictions stay within measured concentration / temperature support. One temperature cannot establish a temperature effect.
Needle and barrel dimensions Required	Internal bore, effective needle flow length and barrel internal diameter in mm.	No automatic geometry estimate. Use supplier or measured dimensions; gauge alone does not define the internal bore.
Target time + available force Required for the full result set	Delivery time in seconds and net force at the plunger in N.	Target time determines required force; available force determines predicted time. Both define viscosity and needle limits. Starting values are examples, not recommendations.
Stopper glide force Measured or assumed	A measured / supplier value, or your assumed low, nominal and high forces.	The initial 1 / 3 / 5 N values are illustrative assumptions, not a literature-derived estimate, universal range or ISO limit. The system evaluates the chosen bounds.
Outlet / tissue pressure Measured or assumed	Choose in-air, measured, literature screening or your own bounds.	In air uses 0 kPa. Human SC screening uses 0–80 kPa from a small insulin study; 40 kPa is an assumed midpoint. Swine screening uses 24 ± 3.4 kPa at 1 mL / 10 s. These are context-specific examples, not universal human limits. Study links and conditions appear beside the pressure selector.
Density Needed for the flow check	Measured density, or a justified water-like approximation.	The starting 1,000 kg/m³ is illustrative. Density is used for Reynolds number, not the force / time calculation.
Stroke / pressure limits, break-loose force and other input ranges Optional	Device limits, measured starting force, and justified minimum / maximum values.	Adds feasibility checks and deterministic bounds. It does not infer missing device limits or calculate a probability of success.

Which data produces each result?

Result	Depends on
Required force + force-versus-time graph	Volume, viscosity, needle bore / length, barrel diameter, glide force and outlet pressure. Target time selects the operating point; available force adds the comparison line.
Predicted delivery time	The same drug / geometry / resistance inputs, plus available plunger force. If force cannot overcome glide friction and outlet pressure, delivery stalls.
Maximum viscosity + minimum needle bore	Volume, target time, available force, geometry, friction and outlet pressure. The bore calculation also uses entered viscosity; the viscosity limit uses entered bore.
Pressure + plunger stroke	Pressure at target: viscosity, needle geometry and volume ÷ target time. Total pressure also includes outlet pressure. Stroke: volume ÷ barrel cross-sectional area.
Feasible concentration range + concentration graph	A confirmed viscosity–concentration curve at the chosen temperature, plus the device / target inputs. With fixed dose, volume changes as dose ÷ concentration. Any entered stroke limit also constrains feasibility. No concentration prediction beyond the supplied data.
Viscosity-versus-concentration / temperature graphs	Your measured concentration, temperature and viscosity points. Multiple suitable temperatures are needed to fit temperature effects. The fitted relationship is empirical, not a measured guarantee.
Best / nominal / worst results	Your nominal inputs and selected low / high bounds. The system evaluates independent combinations; these are bounds within your assumptions, not confidence intervals.

Calculation basis: laminar, Newtonian needle flow (Hagen–Poiseuille), plus glide friction and outlet pressure. Starting transients and full device dynamics are not modelled. ISO 11608-1 does not supply universal values for these assumptions; this tool does not establish ISO compliance.

Preliminary screening: starting inputs are illustrative, not measured product specifications. Unknown glide friction can use an assumed range. Select in-air, measured or literature-guided back pressure, and replace assumptions as evidence becomes available.

Drug · Viscosity model builderFit concentration and temperature data · predict viscosity · apply to injection performance

Measurements

One formulation and consistent viscosity method/shear conditions. Paste rows as concentration (mg/mL), temperature (°C), viscosity (cP). At least four independent concentrations at one temperature, or five independent combinations for two-variable fits.

Concentration, temperature, viscosity

Illustrative example data — replace before product decisions.

I have reviewed the dataset and assumptions for this preliminary use.

Prediction concentration (mg/mL)Prediction temperature (°C)

Predicted viscosity: 5.44 cP at 50 mg/mL and 20 °C.

Applies the selected temperature slice within measured support. The injection calculator uses 81 fitted-curve samples for the concentration ceiling, labelled as model-derived. It does not replace your drug dose or device inputs.

Best-supported fit: Exponential concentration + reciprocal temperature

9 independent conditions · 0 replicate rows averaged by condition. Automatic selection minimizes leave-one-condition-out prediction RMSE (cP); the simplest candidate within 5% of the lowest error is preferred. This is not external validation.

Displayed model

Viscosity vs concentration

● 5 °C● 20 °C · prediction slice● 35 °C

Viscosity vs temperature

● 10 mg/mL● 50 mg/mL · prediction slice● 100 mg/mL

Colored points: condition-mean measurements. Curves: fitted model at each measured temperature/concentration; orange dashed curve: requested prediction slice. Curves stop at the measured region's convex hull; empty areas are not extrapolated.

Candidate	Fit RMSE (cP)	Held-out RMSE (cP)	R² (fit)
Exponential concentration + reciprocal temperature · recommended	0.00604	0.008973	1
Quadratic concentration in log viscosity	0.005822	0.009712	1
Concentration–temperature interaction in log viscosity	0.00695	0.01768	1

Sparse dataset: model selection and prediction error estimates are preliminary. Add independent validation measurements.

Equation, coefficients and excluded models

ln(μ) = 1.812 + 1.801·x + 1.042·z

μ in cP. x = (concentration − 55) / 90. z = (1000 / (temperature + 273.15) − 3.417) / 0.35.

Linear viscosity: The fitted model does not give a positive finite viscosity at this point.

Reciprocal-temperature log-viscosity models have been used in published formulation/injector modeling. Coefficients here are fitted only to your data, not borrowed. Quadratic and interaction candidates are exploratory empirical alternatives. No model is universally best; trends and predictions need experimental review.

1 · Dose and delivery target

Primary calculation

Both results are shown. Available force and target time also define the viscosity and needle limits.

Injection volume sourceVolume per injection

Target delivery time

2 · Drug properties

Injection / measurement temperature

°C

Dynamic viscosity

cP = mPa·s

Fluid density (flow check)

kg/m³

Newtonian formulation at the stated temperature Link viscosity to concentration data

3 · Device and flow path

Stopper glide-force evidence

Assumed lowest glide force

Assumed highest glide force

Preliminary assumptions: 1–5 N is an illustrative starting range, not a supplier specification, universal device range or ISO limit. Replace it with justified bounds. The nominal glide force below must lie within the range. Results automatically include best/worst cases for these assumptions.

Net force available at plunger

Needle internal diameter

Effective needle flow-path length

Syringe / cartridge internal diameter

Stopper glide friction

Outlet / tissue back pressure

kPa

Use measured needle bore and full fluid-path length, not gauge or exposed length alone. Net plunger force excludes upstream mechanism losses; glide friction is subtracted separately. Back pressure = 0 represents injection into air.

Outlet / tissue back-pressure basis

Help choosing difficult inputs

Use supplier dimensions for actual needle bore, barrel diameter and full needle length. Measure viscosity at the intended temperature; use an explicit range if only preliminary estimates exist. Density starts at a water-like assumption of 1,000 kg/m³ for the Reynolds check. Replace it for your formulation.

Glide friction depends on stopper, lubrication, aging, speed and fluid pressure. The illustrative 1–5 N range is an assumption. Published model and friction measurements. A separate animal study shows tissue resistance changes with viscosity and injection rate; a constant pressure is only a screening approximation.

ISO 11608-1 clause review is pending. No estimates here are presented as standard-specified values.

Optional device limits and start-up check

Available plunger stroke

Maximum permitted pressure

kPa

Measured break-loose force at plunger

Break-loose is checked separately against available initial force; start-up delay is not modeled. Enter a measurement under representative loading. No default acceptance limits are assumed.

4 · Minimum / nominal / maximum

Evaluate independent input ranges

NOMINAL ENGINEERING ESTIMATE

Required plunger force

11.4 N

For 1 mL · 10 cP at 20 °C.

Required force at 10 s11.4 N

Time at 20 N4.96 s

Force margin at target time8.57 N

Nominal available force meets the target delivery time in this model; review the range results below.

Force versus delivery time

Teal: required plunger force · orange: available force. Fixed properties and volume; shorter delivery needs higher force.

Maximum viscosity and concentration

Maximum viscosity at fixed 1 mL20.2 cP

Maximum concentration within supplied curveAdd measured curve

Viscosity ceiling uses 20 N and 10 s, with entered friction and back pressure. Unknown inputs use explicit assumptions, not inferred measurements. Concentration search holds injection volume fixed, so drug dose changes with concentration.

Needle bore, pressure and stroke

Minimum internal needle diameter for target time0.176 mm

Required plunger stroke31.6 mm

Fluid pressure at target time266 kPa

Fluid pressure at available force537 kPa

Minimum bore keeps length and other inputs fixed; select a supplier-specified bore at or above this value. Pressure includes needle loss and entered outlet back pressure; stopper friction is excluded from fluid pressure.

Best / nominal / worst within assumed input bounds

Output	Minimum	Nominal	Maximum
Required force (N)	9.43	11.4	13.4
Delivery time (s)	4.43	4.96	5.62
Pressure at target (kPa)	266	266	266
Stroke (mm)	31.6	31.6	31.6
Viscosity ceiling (cP)	17.8	20.2	22.5
Minimum bore (mm)	0.171	0.176	0.182

2 input corners assessed. 0 have no forward-delivery force margin. Maximum corner Reynolds: 137. These are independent bounds, not probabilities.

Model, evidence and ISO status

Engineering estimate for a straight circular needle, Newtonian incompressible liquid, laminar flow, constant net plunger force, constant glide friction and constant back pressure. Excludes entrance/connector losses, compliance, air bubbles, needle insertion, startup transients and hold time. Verify predictions against physical tests.

Equations and sources

Q = V / t; A = πD² / 4; Δp = 128μLQ / (πd⁴); F = Fglide + A(Δp + Pback); stroke = V / A. Internal calculations use SI units. 1 cP = 1 mPa·s.

Published autoinjector force-balance and injection-time model. A constant-friction approximation is less detailed than the measured profiles discussed in this publication.

ISO 11608-1:2022: clause mapping and applicable test-condition review remain pending. No universal force/time limits or ISO conformity claims are applied here. The existing dose-accuracy workspace remains separate.