Hand-Arm Vibration Exposure Calculator

Record the assessment

HSE says the findings of a vibration risk assessment must be recorded, with an action plan for anything needed to comply. The workplace exposure assessment record template records one assessment for one agent, with “other physical agent” among its agent types: who is exposed, the measurement or estimate used and its result, the value you compare it with and its source, the decision and the actions. It supplies no limit values, so enter the ones above with their source. The noise and hand-arm vibration compliance guide covers measurement, control and health surveillance.

What the calculation does

For each tool, the partial exposure is the vibration magnitude multiplied by the square root of the trigger time divided by 8 hours: A(8) = a_hv × √(T ÷ 8 h). This is the formula in Schedule 1 of the 2005 Regulations. The daily exposure is the square root of the sum of the squared partial exposures, which is the same as the Schedule's formula for a day made up of several operations.

HSE equates 2.5 m/s² A(8) with 100 exposure points and 5 m/s² A(8) with 400. Because time enters A(8) under a square root, points follow the square of A(8): points = 100 × (A(8) ÷ 2.5)². For one tool this works out at 2 × a_hv² points for each hour of trigger time. HSE's web pages give the two anchor values and an approximate table, not this formula; the formula reproduces the table exactly at 5, 10 and 15 m/s² (50, 200 and 450 points an hour) and comes within 10% of HSE's approximate figures at the other magnitudes, for example 18 against HSE's “20” at 3 m/s² and 288 against “300” at 12 m/s².

The time for one tool to reach a value is 8 hours × (value ÷ a_hv)². It is shown rounded down to the whole minute, and as “more than 24 h” beyond a day. It assumes that tool alone; when other tools are used the same day, the time left is shorter.

A result appears only when every filled row has a magnitude above 0 and up to 100 m/s², and a time of zero or more; the times for the day may not add up to more than 24 hours. Blank rows are ignored. The action and limit values are compared with the daily figure as shown, to two decimals, so the status never contradicts the number on screen (for example 7.07 m/s² for one hour is 2.4996, shown as 2.50 and treated as reaching 2.5): “at or above” the action value follows the Regulations' wording (“reached or exceeded”), and the limit value is passed only when the figure is above 5.00. Weekly averaging under regulation 6(5) is not calculated.

For whole-body vibration, Schedule 2 evaluates A(8) separately for x, y and z, with k = 1.4 for the horizontal axes and 1.0 for the vertical axis, and the Directive's Annex B takes the highest of 1.4a_wx, 1.4a_wy and a_wz. The calculator applies k to each machine before combining machines axis by axis, then takes the highest axis.

Worked examples

HSE's time limit example. HSE's forestry and arboriculture page says that a mechanical scythe or hand-guided shears might have a vibration emission of around 10 m/s², and that a usage limit of 30 minutes would prevent the action value being exceeded, provided no other vibrating tools are used that day. The arithmetic: 10 × √(0.5 ÷ 8) = 10 × 0.25 = 2.50 m/s² A(8), which is 100 points. The calculator shows 30 min as the time to 2.5 m/s² A(8) and 2 h as the time to 5 m/s² A(8).

Two tools in one day. This is the example in our compliance guide, and the one the form opens with. The magnitudes are assumptions, not measurements. An operator uses a breaker at 9 m/s² for 90 minutes and a grinder at 5 m/s² for 45 minutes.

• Breaker: 9 × √(1.5 ÷ 8) = 3.90 m/s² A(8); 2 × 81 × 1.5 = 243 points
• Grinder: 5 × √(0.75 ÷ 8) = 1.53 m/s² A(8); 2 × 25 × 0.75 = 37.5 points, shown as 38
• Daily: √(3.90² + 1.53²) = 4.19 m/s² A(8); 280.5 points, shown as 281
• The breaker alone reaches 2.5 m/s² A(8) after 37 minutes and 5 m/s² A(8) after 2 h 28 min; the grinder alone after 2 h and 8 h

The daily figure is above the action value and below the limit value. The breaker contributes 243 of the 281 points, so cutting its trigger time or magnitude changes the result most. These are the values the calculator's own functions return for these entries.

Why the result can mislead

The magnitude matters most, because points grow with its square: a tool at 10 m/s² gives four times the points of one at 5 m/s² for the same time. HSE warns that some manufacturer data may underestimate workplace vibration substantially, and that measurement results vary with the operator's technique, the condition of the tool, the material and the measurement method. HSE's typical values are for an initial assessment and the ranges behind them are wide: 7 to 18 m/s² for breakers.

Trigger time is easy to overstate or understate. HSE says it may be only a few minutes in several hours of work with a tool, that employees are unlikely to estimate it accurately themselves, and suggests observing it, for example over half an hour, and scaling up. HSE also found that electronic monitoring systems can differ by up to 20% when monitoring the same task. Halving the time lowers A(8) by only about 29%, because time enters under a square root.

A result below the action value is not a clean bill of health: HSE says the action value is not an entirely safe level, and the Regulations require risk to be reduced as far as is reasonably practicable at any level. The calculator adds no uncertainty margin, covers one day for one person, and does not decide who needs health surveillance.

Where the formulas and values come from

• Directive 2002/44/EC on EUR-Lex, read in the original text and the consolidated version of 26 July 2019, which EUR-Lex listed as current. Article 3 sets 2.5 and 5 m/s² for hand-arm vibration and 0.5 and 1.15 m/s² for whole-body vibration (or, at a Member State's choice, vibration dose values of 9.1 and 21 m/s^1.75). Article 5 covers the programme of measures and the limit value, Article 8 health surveillance, and the Annex the basis of assessment, including the higher value of the two hands.
• The Control of Vibration at Work Regulations 2005 on legislation.gov.uk: regulation 4 (the four values), regulation 6 (control of exposure), regulation 7 (health surveillance), Schedule 1 (hand-arm A(8) formulas) and Schedule 2 (whole-body A(8) and the k factors). For regulations 4 and 6 and both Schedules, the site showed no known outstanding changes.
• HSE, the hand-arm vibration exposure calculator: partial and daily exposure in A(8) and points, points per hour, and time to the action value (2.5 m/s² A(8) or 100 points) and limit value (5 m/s² A(8) or 400 points).
• HSE, vibration risk assessment: typical vibration levels and initial values (Table 1), the exposure points table (Table 2), trigger time and the warning about manufacturer data.
• HSE, hand-arm vibration in forestry and arboriculture (the 10 m/s² and 30-minute example), measurement and monitoring, hand-arm vibration in foundries and the whole-body vibration regulations page.

All of these pages were opened on 22 October 2026. They are sources of the law and of HSE's method; they do not validate this calculator or any particular result.

What we could not verify (22 October 2026)

• We did not download HSE's spreadsheet calculator, so we could not compare its formulas, rounding or display with ours.
• We did not open HSE's guidance book L140 or its leaflet INDG175, which are PDF files and contain HSE's own worked examples. The points formula above is derived from the anchor values and table on HSE's web pages.
• We did not read ISO 5349-1, ISO 5349-2 or ISO 2631-1, which are paid standards. Frequency weighting, measurement and uncertainty are outside this calculator.
• Schedule 2's formula for several whole-body operations is printed without k. We applied k to each operation, as in the Schedule's single-operation formula and the Directive's Annex B; we did not find guidance that settles the point on the pages we read.
• We did not check how each EU Member State transposed the Directive, including which ones use vibration dose values for whole-body vibration, or the rules outside Great Britain, and we did not look for an exposure points system for whole-body vibration, so none is included.